Question

Show whether rolles theorem can be applied to f(X). if it can, determine any values of c in the interval [0,2pi] for which f'(c) = 0 f(x) = cos x

Answer 1

In the interval given, notice that f(pi/2)=cos(pi/2)=0
and notice that f(3pi/2)=0.
You have to notice that stuff.

It is : 0 < pi/2 < 3pi/2 < 2pi, so the said examples are within the boudaries given.
f(x)=cosx is both continuous and is differentiable.

So, Rolls Theorem can be used in f(x).