Question

The least value of the function f(x) = 2 cos x + x in the closed interval `[0, π/2]` is:

Options

• 2

• `π/6 + sqrt3`

• `π/2`

• The least value does not exist.

Answer 1

`π/2`

Explanation:

f(x) = 2 cos x + x, x ∈ `[0, π/2]`

f'(x) = −2 sin x + 1

Let f'(x) = 0

x = `π/6 ∈ [0, π/2]`

f(0) = 2

`"f"(π/6) = π/6 + sqrt3`

`"f"(π/2) = π/2`

Least value of f(x) is `π/2` at x = `π/2`.