Cracking The Ap Calculus ab Exam 2018

(3)The  y-coordinates   of  each    critical    point   are found   by  plugging    the x-value into    the original

equation.

As always, this stuff will sink in better if we try a few examples.

Example 1: Sketch the equation y = x^3 − 12x.

Step 1: Find the x-intercepts.

x^3     −   12x =   0

x(x^2   −   12) =   0

x(x −    )  (x  +    )  =   0

x   =   0,  ±   

The curve has x-intercepts at , and (0, 0).

Next, find the y-intercepts.