Maxima and Minima of tan(sinx + sin3x) on (-pi,pi)

[wildcat12]

Homework Statement

Find the maxima and minima of the function f(x)=tan(sinx + sin3x) on the interval (-pi,pi)

Homework Equations

The Attempt at a Solution

I found the derivative as sec^2x (sinx +sin3x) (cosx + cos3x) and when i set it equal to zero i found critical points at Sin=pi/2, and cos=pi/2

 

[micromass]

Your derivative is incorrect. The derivative of sin(3x) is not cos(3x)...

 

[wildcat12]

Wait i typed that part wrong. i had derivative of sin(3x) as 3Cos(3x)

 

[micromass]

Good, so your derivative is

$$\frac{\cos(x)+3\cos(3x)}{\cos^2(\sin(x)+\sin(3x))}$$

This can only become zero if $$\cos(x)+3\cos(3x)$$. So you'll need to solve the equation $$\cos(x)=-3\cos(3x)$$. I believe there will be infinitly many solutions to this, but I'm not sure...