Cracking The Ap Calculus ab Exam 2018

If we call the length of the field y and the width of the field x, the formula for the area of the field becomes

A   =   xy

The perimeter of the fencing is equal to the sum of two widths and the length.

2 x +   y   =   3,000

Now solve this second equation for y.

y   =   3,000   −   2x

When you plug this expression into the formula for the area, you get a formula for A in terms of x.

A   =   x(3,000 −   2x) =   3,000x  −   2x^2

Next, take the derivative, set it equal to zero, and solve for x.

    =   3,000   −   4x  =   0

x   =   750

Let’s check to make sure it’s a maximum. Find the second derivative.

= −4

Because we have a negative result, x = 750 is a maximum. Finally, if we plug in x = 750 and solve for y,
we find that y = 1,500. The largest field will measure 750 feet by 1,500 feet.

PROBLEM 2. A poster is to contain 100 square inches of picture surrounded by a 4-inch margin at the top