Cracking The Ap Calculus ab Exam 2018

This is positive when x is positive, so the minimum surface area occurs when x = 8. The dimensions of
the box should be 8 inches by 8 inches by 4 inches.

PROBLEM 4. Find the point on the curve y = that is a minimum distance from the point (4, 0).

Answer: First, make that sketch.

Using the distance formula, we get

D^2     =   (x  −   4)^2    +   (y  −   0)^2    =   x^2     −   8x  +   16  +   y^2

Because y = ,

D^2     =   x^2     −   8x  +   16  +   x   =   x^2     −   7x  +   16

Next, let L = D^2 . We can do this because the minimum value of D^2 will occur at the same value of x as the

minimum value of D. Therefore, it’s simpler to minimize D^2 rather than D (because we won’t have to take
a square root!).

L   =   x^2     −   7x  +   16

Now, take the derivative and set it equal to zero.