Question

What are the critical points for xtanx?
Derivative of that is = x(sec^2 x) + tanx

Answer 1

Critical points of an equation are the zeroes of its first derivative. Since you have already provided me with the derivative (thanks for saving me the effort :) ), I am just going to start the process.

tan (x) + x(sec^2(x)) = 0

Solving this equation (using a graphing calculator set to radians), it is only true when x = 0.

So, 0 is a critical point of this function.

Hope this helped!