1. Base = x Height = f(x) = y = x2
What is the formula for the area of a triangle?
Area = ½ * Base * Height
We need to rewrite the Base and Height as an expression with the variable x.
Base
( 0, y)
Base = x
Height = f(x) = y = x2
Height
( 0, 0)

2. What x coordinate in Quadrant 1 will maximize the area?
What is the formula for the area of a rectangle?
Area = Base * Height = Length * Width
We need to rewrite the Base and Height as an expression with the variable x.
| 2x | y
Height
Base =
| 2x |
Height = y
We need to solve the circle formula for y. x x
We need absolute value bars because x could be a negative.
Base
There is no + because the height must be positive.
What x coordinate in Quadrant 1 will maximize the area?

3. Time rowing + Time walking
b =
12 - x
T(x) =
Time rowing + Time walking
Row Dist. = D
a =
= c
Rowing time.
Walking time.
Right triangle.
a2 + b2 = c2
Find D in the rt triangle.
We are going to need the formula D = r * t. We will need to solve this formula for t.

4. What is the fastest time to go from the island to town?
Graph the function and find the relative minimum!
We need to find the domain for x.
What is the smallest value for x?
0; this is the X min
What is the largest value for x?
12; this is the X max
What is the largest value for y?
If you land 1.5 miles from point P, it will take you 2.93 hours to get to town.
Rowing all the way to town. x = 12
5; this is the Y max

5. What is the formula for the volume of a box?
36 in.
Volume = Length * Width * Height x x
We need to rewrite the Base, Width, and Height as an expression with the variable x. x x
36 – 2x
(36 – 2x )
(36 – 2x ) x x x x x
What x by x square do you need to cut out to generate the maximum volume of the box? x
Max Volume
(36 – 2x )
(36 – 2x )