Y=XSIN(PI X)Y'=SIN(PI X)+ PI XCOS(PI X)I don't know who to solve for the critical numbers because I don't know how to factor this.Thanks!

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.

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.

Most graphing calculators have a utility which finds roots of functions. It asks for an initial guess and then uses a built in algorithm (presumably Newton's Method). This utility is usually available when you graph functions.

In your case you would input f(x) = sin(px) + px cos(px).

## 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.