At what points in the interval [0, 2π], does the function sin 2x attain its maximum value?

Question

Philoid · Accepted Answer

It is given that f (x) = sin2x, x ∈ [0, 2π]

f’(x) = 2cos2x

Now, f’(x) = 0

⇒ cos2x = 0

⇒ 2x = 0

⇒ x =

Now, we evaluate the value of f at critical point x = and at end points of the interval [0, 2π]

f’ =

f(0) = sin0, f(2π) = sin2π = 0

Therefore, we have the absolute maximum value of f on [0, 2π] is 1 occurring at

x = and x =.