Barrons AP Calculus - David Bock

(B) When f ′ is positive, f increases. By the Fundamental Theorem of Calculus, f′ (x) = 1 − 2
(cos x)^3. Graph f ′ in [0, 2π] × [−2, 4]. It is clear that f ′ > 0 on the interval a < x < b. Using
the calculator to solve 1 − 2(cos x)^3 = 0 yields a = 0.654 and b = 5.629.