What are the coordinates of the relative extrema?

Question

The derivative of function f is given by f'(x) = ((cos^2x)/x)-0.2 Note that this is the equation for the derivative of f, not for the function f itself. Find the x-coordinates of relative extrema of f between x=0 and x=10

Answer 1

To find the relative extrema in the given interval [0, 10] you need to solve the equation 

f'(x)=0 for x, that is

((cos^2x)/x)-0.2=0.

If you solve this equation, you get two points x=π/2 and x=5π/2 from [0, 10]. These are what the question asks for.