With other problems such as Y= 2X^3 + 3X^2, I can easily factor the deriviate: Y'= 6X^2 + 6X and set it equal to zero. With the trig derivative, I don't know how to finish the problem.

Ideas: Critical points are at y' = 0

Therefore, solving y' = sin(πx) + πxcos(πx) = 0 gives you the answer.

## Comments

How do I find all the x values that give me zero?

There are infinite number of answers. But most likely you are given an interval for x. Therefore, you can use a graphing calculator to get finite number of answers inside the interval.

Y1 = sin(px) + pxcos(px)

Finding zero in the interval gives you all the answers.