Question

The maximum value of `["x"("x" − 1) + 1]^(1/3)`, 0 ≤ x ≤ 1 is:

Options

• 0

• `1/2`

• 1

• `root3(1/3)`

Answer 1

1

Explanation:

Let f(x) = `["x"("x" − 1) + 1]^(1/3)`, 0 ≤ x ≤ 1 

f'(x) = `(2"x" - 1)/(3("x"^2 - "x" + 1)^(2/3))` let f'(x) = 0 ⇒ x = `1/2 ∈ [0, 1]`

f(0) = 1, `"f"(1/2) = (3/4)^(1/3)` and f(1) = 1

∴ Maximum value of f(x) is 1.