Cracking The Ap Calculus ab Exam 2018

At  x   =    ,  y   =       ≈   −0.385

Now it’s time to check the endpoints of the interval.

At  x   =   −3, y   =   −24

At  x   =   3,  y   =   24

We can see that the function actually has a lower value at x = −3 than at its “minimum” when x = .

Similarly, the function has a higher value at x = 3 than at its “maximum” of x = − . This means that the

function has a “local minimum” at x = , and an “absolute minimum” when x = −3. And, the function has

a “local maximum” at x = − , and an “absolute maximum” at x = 3.

Example 6: A rectangle is to be inscribed in a semicircle with radius 4, with one side on the semicircle’s
diameter. What is the largest area this rectangle can have?

Let’s look at this on the coordinate axes. The equation for a circle of radius 4, centered at the origin, is x^2

• y^2 = 16; a semicircle has the equation y = . Our rectangle can then be expressed as a function

of x, where the height is and the base is 2x. See the following figure:

The area of the rectangle is: A = 2x . Let’s take the derivative of the area.