( 0, y)

( 0, 0)

What is the formula for the area of a triangle?

Area = ½ * Base * Height

_____________2

1xA

We need to rewrite the Base and Height as an expression with the variable x.

Height

Base

Base = x Height = f(x) = y = x2

32

2

1

2

1xxxxA

What is the formula for the area of a rectangle?Area = Base * Height = Length * Width

_________________xA

We need to rewrite the Base and Height as an expression with the variable x.

Height

Base

Base = | 2x |

x x Height = y

We need to solve the circle formula for y.

3622 yx22 36 xy

22 36 xy 236 xy

There is no + because the height must be positive.

2362 xxxA

| 2x | y

What x coordinate in Quadrant 1 will maximize the area?

We need absolute value bars because x could be a negative.

T(x) = Time rowing + Time walking

We are going to need the formula D = r * t. We will need to solve this formula for t.

Rowing time. Walking time.

r

tr

r

D

trD

r

Dt

r

Dt

3

D

Row Dist. = D

Right triangle.a2 + b2 = c2

a =

b =

= c

Find D in the rt triangle.

Dx

Dx

2

222

4

2

3

4 2x

12 - x

r

Dt

5

D

5

12 x

5

12

3

4 2 xxxT

What is the fastest time to go from the island to town?

5

12

3

4 2 xxxT

Graph the function and find the relative minimum!

We need to find the domain for x.

What is the smallest value for x?

What is the largest value for x?

0; this is the X min

12; this is the X max

What is the largest value for y?

Rowing all the way to town. x = 12

5; this is the Y max

If you land 1.5 miles from point P, it will take you 2.93 hours to get to

town.

What is the formula for the volume of a box?

Volume = Length * Width * Height

__________________________ xV

We need to rewrite the Base, Width, and Height as an expression with the variable x.

36 in.

x

x

x

x x

x

x x

x 36 – 2x (36 – 2x ) (36 – 2x )

x

(36 – 2x )

(36 – 2x )

2236 xxxV What x by x square do you need to cut out to generate the maximum volume of the box?

Max Volume