Question

Find the maximum and minimum values of

f(x) = (-x+2 sin x) on [0, 2π]

Answer 1

By finding the general solution, we get x = π/3 and x = 5π/3

Now, by finding the second derivative, we get that f"(π/3)<0 and f"(5π/3)>0

Therefore, max. value is (-π/3+√3) at x = π/3 and min. value is (5π/3+√3) at x = 5π/3