04/19/23 Perkins

AP Calculus AB

Day 9Section 3.6

Sketch 2 6 5f x x x

crit #'s: 3x

Include intercepts, asymptotes, extrema, inflection points, and intervals of concavity.

crit #'s: none

2 6 5g x x x Compare to What’s the difference between f(x) and g(x)?The abs val makes all the negative parts of g(x) reflect above the x-axis.

' 2 6g x x

'' 2g x

x-int y-int

5y 2 6 5 0x x 5 1 0x x

1, 5x

Parabola opening upward (no asymptotes)

Always concave up

Rel min at (3, -4)

10

5

-5

-10

-10 10

g(x)

10

5

-5

-10

-10 10

2 6 5f x x x 2 6 5g x x x x-int: x = 1 and 5

y-int: y = 5

conc up ,1 and 5,

Rel min at (1, 0)

Rel min at (5, 0)

Inf pts at (1, 0) and (5, 0)

Rel max at (3, 4)

conc down 1,5

f(x)

Perkins

AP Calculus AB

Day 9Section 3.6

Sketch 2 6 5f x x x

Include intercepts, asymptotes, extrema, inflection points, and intervals of concavity.

10

5

-5

-10

-10 10

10

5

-5

-10

-10 10