Question

How do I find the numbers `c` that satisfy Rolle's Theorem for `f(x)=cos(2x)` on the interval `[pi/8,(7pi)/8]` ?

Answer 1

Find `c` in `( pi/8, (7 pi)/8)` to solve `f'(c) = 0`.

Since `f'(x) = -2sin(2x)` this amounts to solving

`-2sin(2x) = 0` for solutions in `( pi/8, (7 pi)/8)`