1. ( 0, y) ( 0, 0) 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. Height Base Base = xHeight = f(x) = y = x 2

2. 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. Height Base Base = | 2x | x x Height = y We need to solve the circle formula for y. There is no + because the height must be positive. | 2x | y What x coordinate in Quadrant 1 will maximize the area? We need absolute value bars because x could be a negative.

3. 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. Row Dist. = D Right triangle. a 2 + b 2 = c 2 a = b = = c Find D in the rt triangle. 12 - x

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? 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.

5. What is the formula for the volume of a box? Volume = Length * Width * Height 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 x36 – 2x(36 – 2x ) x What x by x square do you need to cut out to generate the maximum volume of the box? Max Volume