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Math 1210 Salt Lake Community College Spring 2015

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Page 1: Math1210 Salt%Lake%Community%College% Spring2015parshurambudhathoki.weebly.com/uploads/3/8/0/2/38024669/chapte… · 4:ApplicaonofDifferenaon • 4.1:&Maximum&and&Minimum&Values.&

Math  1210  Salt  Lake  Community  College  

Spring  2015

Page 2: Math1210 Salt%Lake%Community%College% Spring2015parshurambudhathoki.weebly.com/uploads/3/8/0/2/38024669/chapte… · 4:ApplicaonofDifferenaon • 4.1:&Maximum&and&Minimum&Values.&

Review  

Page 3: Math1210 Salt%Lake%Community%College% Spring2015parshurambudhathoki.weebly.com/uploads/3/8/0/2/38024669/chapte… · 4:ApplicaonofDifferenaon • 4.1:&Maximum&and&Minimum&Values.&

4:Applica>on  of  Differen>a>on

•  4.1:  Maximum  and  Minimum  Values.  •  4.2:  The  Mean  Value  Theorem  •  4.3:  How  Deriva=ve  Affect  the  Shape  of  a  Graph  •  4.4:  Indeterminate  Forms    and  l’Hospital’s  Rule  •  4.5:  Summary  of  Curve  Sketching    •  4.7:  Op=miza=on  Problem  •  4.8:  Newton’s  Method  •  4.9:  An=deriva=ves  

Page 4: Math1210 Salt%Lake%Community%College% Spring2015parshurambudhathoki.weebly.com/uploads/3/8/0/2/38024669/chapte… · 4:ApplicaonofDifferenaon • 4.1:&Maximum&and&Minimum&Values.&

4.1:Maximums  and  Minimum  Values

Page 5: Math1210 Salt%Lake%Community%College% Spring2015parshurambudhathoki.weebly.com/uploads/3/8/0/2/38024669/chapte… · 4:ApplicaonofDifferenaon • 4.1:&Maximum&and&Minimum&Values.&

4.1:Maximums  and  Minimum  Values

Page 6: Math1210 Salt%Lake%Community%College% Spring2015parshurambudhathoki.weebly.com/uploads/3/8/0/2/38024669/chapte… · 4:ApplicaonofDifferenaon • 4.1:&Maximum&and&Minimum&Values.&

4.1:Maximums  and  Minimum  Values

Page 7: Math1210 Salt%Lake%Community%College% Spring2015parshurambudhathoki.weebly.com/uploads/3/8/0/2/38024669/chapte… · 4:ApplicaonofDifferenaon • 4.1:&Maximum&and&Minimum&Values.&

4.1:Maximums  and  Minimum  Values

Page 8: Math1210 Salt%Lake%Community%College% Spring2015parshurambudhathoki.weebly.com/uploads/3/8/0/2/38024669/chapte… · 4:ApplicaonofDifferenaon • 4.1:&Maximum&and&Minimum&Values.&

4.1:Maximums  and  Minimum  Values

Page 9: Math1210 Salt%Lake%Community%College% Spring2015parshurambudhathoki.weebly.com/uploads/3/8/0/2/38024669/chapte… · 4:ApplicaonofDifferenaon • 4.1:&Maximum&and&Minimum&Values.&

4.1:Maximums  and  Minimum  Values

Page 10: Math1210 Salt%Lake%Community%College% Spring2015parshurambudhathoki.weebly.com/uploads/3/8/0/2/38024669/chapte… · 4:ApplicaonofDifferenaon • 4.1:&Maximum&and&Minimum&Values.&

4.1:Maximums  and  Minimum  Values

Page 11: Math1210 Salt%Lake%Community%College% Spring2015parshurambudhathoki.weebly.com/uploads/3/8/0/2/38024669/chapte… · 4:ApplicaonofDifferenaon • 4.1:&Maximum&and&Minimum&Values.&

4.1:Maximums  and  Minimum  Values

Page 12: Math1210 Salt%Lake%Community%College% Spring2015parshurambudhathoki.weebly.com/uploads/3/8/0/2/38024669/chapte… · 4:ApplicaonofDifferenaon • 4.1:&Maximum&and&Minimum&Values.&

4.1:Maximums  and  Minimum  Values

Page 13: Math1210 Salt%Lake%Community%College% Spring2015parshurambudhathoki.weebly.com/uploads/3/8/0/2/38024669/chapte… · 4:ApplicaonofDifferenaon • 4.1:&Maximum&and&Minimum&Values.&

4.1:Maximums  and  Minimum  Values

Page 14: Math1210 Salt%Lake%Community%College% Spring2015parshurambudhathoki.weebly.com/uploads/3/8/0/2/38024669/chapte… · 4:ApplicaonofDifferenaon • 4.1:&Maximum&and&Minimum&Values.&

4.1:Maximums  and  Minimum  Values

Page 15: Math1210 Salt%Lake%Community%College% Spring2015parshurambudhathoki.weebly.com/uploads/3/8/0/2/38024669/chapte… · 4:ApplicaonofDifferenaon • 4.1:&Maximum&and&Minimum&Values.&

4.1:Maximums  and  Minimum  Values

Page 16: Math1210 Salt%Lake%Community%College% Spring2015parshurambudhathoki.weebly.com/uploads/3/8/0/2/38024669/chapte… · 4:ApplicaonofDifferenaon • 4.1:&Maximum&and&Minimum&Values.&

4.1:Maximums  and  Minimum  Values

Page 17: Math1210 Salt%Lake%Community%College% Spring2015parshurambudhathoki.weebly.com/uploads/3/8/0/2/38024669/chapte… · 4:ApplicaonofDifferenaon • 4.1:&Maximum&and&Minimum&Values.&

4.1:Maximums  and  Minimum  Values

Page 18: Math1210 Salt%Lake%Community%College% Spring2015parshurambudhathoki.weebly.com/uploads/3/8/0/2/38024669/chapte… · 4:ApplicaonofDifferenaon • 4.1:&Maximum&and&Minimum&Values.&
Page 19: Math1210 Salt%Lake%Community%College% Spring2015parshurambudhathoki.weebly.com/uploads/3/8/0/2/38024669/chapte… · 4:ApplicaonofDifferenaon • 4.1:&Maximum&and&Minimum&Values.&

4.2:Mean  Value  Theorem

Page 20: Math1210 Salt%Lake%Community%College% Spring2015parshurambudhathoki.weebly.com/uploads/3/8/0/2/38024669/chapte… · 4:ApplicaonofDifferenaon • 4.1:&Maximum&and&Minimum&Values.&

4.2:Mean  Value  Theorem

Page 21: Math1210 Salt%Lake%Community%College% Spring2015parshurambudhathoki.weebly.com/uploads/3/8/0/2/38024669/chapte… · 4:ApplicaonofDifferenaon • 4.1:&Maximum&and&Minimum&Values.&

4.2:Mean  Value  Theorem

Page 22: Math1210 Salt%Lake%Community%College% Spring2015parshurambudhathoki.weebly.com/uploads/3/8/0/2/38024669/chapte… · 4:ApplicaonofDifferenaon • 4.1:&Maximum&and&Minimum&Values.&

4.2:Mean  Value  Theorem

Page 23: Math1210 Salt%Lake%Community%College% Spring2015parshurambudhathoki.weebly.com/uploads/3/8/0/2/38024669/chapte… · 4:ApplicaonofDifferenaon • 4.1:&Maximum&and&Minimum&Values.&

4.2:Mean  Value  Theorem

Page 24: Math1210 Salt%Lake%Community%College% Spring2015parshurambudhathoki.weebly.com/uploads/3/8/0/2/38024669/chapte… · 4:ApplicaonofDifferenaon • 4.1:&Maximum&and&Minimum&Values.&

4.2:Mean  Value  Theorem

Page 25: Math1210 Salt%Lake%Community%College% Spring2015parshurambudhathoki.weebly.com/uploads/3/8/0/2/38024669/chapte… · 4:ApplicaonofDifferenaon • 4.1:&Maximum&and&Minimum&Values.&

4.2:Mean  Value  Theorem

Page 26: Math1210 Salt%Lake%Community%College% Spring2015parshurambudhathoki.weebly.com/uploads/3/8/0/2/38024669/chapte… · 4:ApplicaonofDifferenaon • 4.1:&Maximum&and&Minimum&Values.&

4.2:Mean  Value  Theorem

Page 27: Math1210 Salt%Lake%Community%College% Spring2015parshurambudhathoki.weebly.com/uploads/3/8/0/2/38024669/chapte… · 4:ApplicaonofDifferenaon • 4.1:&Maximum&and&Minimum&Values.&

4.2:Mean  Value  Theorem

Page 28: Math1210 Salt%Lake%Community%College% Spring2015parshurambudhathoki.weebly.com/uploads/3/8/0/2/38024669/chapte… · 4:ApplicaonofDifferenaon • 4.1:&Maximum&and&Minimum&Values.&

4.2:Mean  Value  Theorem

Page 29: Math1210 Salt%Lake%Community%College% Spring2015parshurambudhathoki.weebly.com/uploads/3/8/0/2/38024669/chapte… · 4:ApplicaonofDifferenaon • 4.1:&Maximum&and&Minimum&Values.&
Page 30: Math1210 Salt%Lake%Community%College% Spring2015parshurambudhathoki.weebly.com/uploads/3/8/0/2/38024669/chapte… · 4:ApplicaonofDifferenaon • 4.1:&Maximum&and&Minimum&Values.&

4.3:Deriva>ve  and  shape  of  a  graph.

Page 31: Math1210 Salt%Lake%Community%College% Spring2015parshurambudhathoki.weebly.com/uploads/3/8/0/2/38024669/chapte… · 4:ApplicaonofDifferenaon • 4.1:&Maximum&and&Minimum&Values.&

4.3:Deriva>ve  and  shape  of  a  graph.

Page 32: Math1210 Salt%Lake%Community%College% Spring2015parshurambudhathoki.weebly.com/uploads/3/8/0/2/38024669/chapte… · 4:ApplicaonofDifferenaon • 4.1:&Maximum&and&Minimum&Values.&

4.3:Deriva>ve  and  shape  of  a  graph.

Page 33: Math1210 Salt%Lake%Community%College% Spring2015parshurambudhathoki.weebly.com/uploads/3/8/0/2/38024669/chapte… · 4:ApplicaonofDifferenaon • 4.1:&Maximum&and&Minimum&Values.&

4.3:Deriva>ve  and  shape  of  a  graph.

Page 34: Math1210 Salt%Lake%Community%College% Spring2015parshurambudhathoki.weebly.com/uploads/3/8/0/2/38024669/chapte… · 4:ApplicaonofDifferenaon • 4.1:&Maximum&and&Minimum&Values.&

4.3:Deriva>ve  and  shape  of  a  graph.

Page 35: Math1210 Salt%Lake%Community%College% Spring2015parshurambudhathoki.weebly.com/uploads/3/8/0/2/38024669/chapte… · 4:ApplicaonofDifferenaon • 4.1:&Maximum&and&Minimum&Values.&

4.3:Deriva>ve  and  shape  of  a  graph.

Page 36: Math1210 Salt%Lake%Community%College% Spring2015parshurambudhathoki.weebly.com/uploads/3/8/0/2/38024669/chapte… · 4:ApplicaonofDifferenaon • 4.1:&Maximum&and&Minimum&Values.&

4.3:Deriva>ve  and  shape  of  a  graph.

Page 37: Math1210 Salt%Lake%Community%College% Spring2015parshurambudhathoki.weebly.com/uploads/3/8/0/2/38024669/chapte… · 4:ApplicaonofDifferenaon • 4.1:&Maximum&and&Minimum&Values.&

4.3:Deriva>ve  and  shape  of  a  graph.

Page 38: Math1210 Salt%Lake%Community%College% Spring2015parshurambudhathoki.weebly.com/uploads/3/8/0/2/38024669/chapte… · 4:ApplicaonofDifferenaon • 4.1:&Maximum&and&Minimum&Values.&

4.3:Deriva>ve  and  shape  of  a  graph.

Page 39: Math1210 Salt%Lake%Community%College% Spring2015parshurambudhathoki.weebly.com/uploads/3/8/0/2/38024669/chapte… · 4:ApplicaonofDifferenaon • 4.1:&Maximum&and&Minimum&Values.&

4.3:Deriva>ve  and  shape  of  a  graph.

Page 40: Math1210 Salt%Lake%Community%College% Spring2015parshurambudhathoki.weebly.com/uploads/3/8/0/2/38024669/chapte… · 4:ApplicaonofDifferenaon • 4.1:&Maximum&and&Minimum&Values.&

4.3:Deriva>ve  and  shape  of  a  graph.

Page 41: Math1210 Salt%Lake%Community%College% Spring2015parshurambudhathoki.weebly.com/uploads/3/8/0/2/38024669/chapte… · 4:ApplicaonofDifferenaon • 4.1:&Maximum&and&Minimum&Values.&

4.3:Deriva>ve  and  shape  of  a  graph.

Page 42: Math1210 Salt%Lake%Community%College% Spring2015parshurambudhathoki.weebly.com/uploads/3/8/0/2/38024669/chapte… · 4:ApplicaonofDifferenaon • 4.1:&Maximum&and&Minimum&Values.&

4.3:Deriva>ve  and  shape  of  a  graph.

Page 43: Math1210 Salt%Lake%Community%College% Spring2015parshurambudhathoki.weebly.com/uploads/3/8/0/2/38024669/chapte… · 4:ApplicaonofDifferenaon • 4.1:&Maximum&and&Minimum&Values.&

4.3:Deriva>ve  and  shape  of  a  graph.

Page 44: Math1210 Salt%Lake%Community%College% Spring2015parshurambudhathoki.weebly.com/uploads/3/8/0/2/38024669/chapte… · 4:ApplicaonofDifferenaon • 4.1:&Maximum&and&Minimum&Values.&
Page 45: Math1210 Salt%Lake%Community%College% Spring2015parshurambudhathoki.weebly.com/uploads/3/8/0/2/38024669/chapte… · 4:ApplicaonofDifferenaon • 4.1:&Maximum&and&Minimum&Values.&

4.4:Indeterminate  Forms  and  l’Hospital’s  Rule

Page 46: Math1210 Salt%Lake%Community%College% Spring2015parshurambudhathoki.weebly.com/uploads/3/8/0/2/38024669/chapte… · 4:ApplicaonofDifferenaon • 4.1:&Maximum&and&Minimum&Values.&

4.4:Indeterminate  Forms  and  l’Hospital’s  Rule

Page 47: Math1210 Salt%Lake%Community%College% Spring2015parshurambudhathoki.weebly.com/uploads/3/8/0/2/38024669/chapte… · 4:ApplicaonofDifferenaon • 4.1:&Maximum&and&Minimum&Values.&

4.4:Indeterminate  Forms  and  l’Hospital’s  Rule

Page 48: Math1210 Salt%Lake%Community%College% Spring2015parshurambudhathoki.weebly.com/uploads/3/8/0/2/38024669/chapte… · 4:ApplicaonofDifferenaon • 4.1:&Maximum&and&Minimum&Values.&

4.4:Indeterminate  Forms  and  l’Hospital’s  Rule

Page 49: Math1210 Salt%Lake%Community%College% Spring2015parshurambudhathoki.weebly.com/uploads/3/8/0/2/38024669/chapte… · 4:ApplicaonofDifferenaon • 4.1:&Maximum&and&Minimum&Values.&

4.4:Indeterminate  Forms  and  l’Hospital’s  Rule

Page 50: Math1210 Salt%Lake%Community%College% Spring2015parshurambudhathoki.weebly.com/uploads/3/8/0/2/38024669/chapte… · 4:ApplicaonofDifferenaon • 4.1:&Maximum&and&Minimum&Values.&

4.4:Indeterminate  Forms  and  l’Hospital’s  Rule

Page 51: Math1210 Salt%Lake%Community%College% Spring2015parshurambudhathoki.weebly.com/uploads/3/8/0/2/38024669/chapte… · 4:ApplicaonofDifferenaon • 4.1:&Maximum&and&Minimum&Values.&

4.4:Indeterminate  Forms  and  l’Hospital’s  Rule

Page 52: Math1210 Salt%Lake%Community%College% Spring2015parshurambudhathoki.weebly.com/uploads/3/8/0/2/38024669/chapte… · 4:ApplicaonofDifferenaon • 4.1:&Maximum&and&Minimum&Values.&

4.4:Indeterminate  Forms  and  l’Hospital’s  Rule

Page 53: Math1210 Salt%Lake%Community%College% Spring2015parshurambudhathoki.weebly.com/uploads/3/8/0/2/38024669/chapte… · 4:ApplicaonofDifferenaon • 4.1:&Maximum&and&Minimum&Values.&

4.4:Indeterminate  Forms  and  l’Hospital’s  Rule

Page 54: Math1210 Salt%Lake%Community%College% Spring2015parshurambudhathoki.weebly.com/uploads/3/8/0/2/38024669/chapte… · 4:ApplicaonofDifferenaon • 4.1:&Maximum&and&Minimum&Values.&

4.4:Indeterminate  Forms  and  l’Hospital’s  Rule

Page 55: Math1210 Salt%Lake%Community%College% Spring2015parshurambudhathoki.weebly.com/uploads/3/8/0/2/38024669/chapte… · 4:ApplicaonofDifferenaon • 4.1:&Maximum&and&Minimum&Values.&

4.4:Indeterminate  Forms  and  l’Hospital’s  Rule

Page 56: Math1210 Salt%Lake%Community%College% Spring2015parshurambudhathoki.weebly.com/uploads/3/8/0/2/38024669/chapte… · 4:ApplicaonofDifferenaon • 4.1:&Maximum&and&Minimum&Values.&
Page 57: Math1210 Salt%Lake%Community%College% Spring2015parshurambudhathoki.weebly.com/uploads/3/8/0/2/38024669/chapte… · 4:ApplicaonofDifferenaon • 4.1:&Maximum&and&Minimum&Values.&

4.5:Curve  Sketching  

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4.5:Curve  Sketching  

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4.5:Curve  Sketching  

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4.5:Curve  Sketching  

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4.7:Op>miza>on  Problems  

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4.7:Op>miza>on  Problems  

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4.7:Op>miza>on  Problems  

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4.7:Op>miza>on  Problems  

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4.7:Op>miza>on  Problems  

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4.7:Op>miza>on  Problems  

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4.7:Op>miza>on  Problems  

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4.9:An>deriva>ves

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4.9:An>deriva>ves

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4.9:An>deriva>ves

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4.9:An>deriva>ves

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4.9:An>deriva>ves

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4.9:An>deriva>ves

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4.9:An>deriva>ves

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4.9:An>deriva>ves

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