Determine whether Rolle's Theorem applies to the following function on the given interval. If so, find the point(s) that are guaranteed to exist by Rolle's Theorem.
$$f(x)=\cos4x$$ on$$[\frac{\pi}{ 8 },\frac{ 3\pi }{ 8}]$$

Question

Determine whether Rolle's Theorem applies to the following function on the given interval. If so, find the point(s) that are guaranteed to exist by Rolle's Theorem.
$$f(x)=\cos4x$$ on$$[\frac{\pi}{ 8 },\frac{ 3\pi }{ 8}]$$

anonymous · Answer

check to see if $\cos(\frac{4\pi}{8})=\cos(\frac{12\pi}{8})$

anonymous · Answer

$$\cos(\frac{4\pi}{8})=\cos(\frac{\pi}{2})=0$$ and 
$$\cos(\frac{12\pi}{8})=\cos(\frac{3\pi}{2})=0$$ so you are good to go

anonymous · Answer

take the derivative, set it equal to zero, and solve for $x$ to finish the question

anonymous · Answer

the derivative would be -4sin4x right?