Question

Find the absolute max or min of f(x) = x + sin2x, ∀ x ∈ [0, 2π]

Answer 1

Given f(x) = x + sin2x, ∀ x ∈ [0, 2π]

⇒ f'(x) = 1 + 2cos2x

Now, f'(x) = 0 gives 1 + 2cos 2x = 0

⇒ cos 2x = – 1/2

⇒ 2x = 2π/3 , 4π/3

⇒ x = π/3 , 2π/3

Therefore, the abolute max value = 2π and absolute min value = 0