Question

The function f(x) = xe^{x(1 − x)}, x ∈ R, is ______.

Options

• increasing in `(−1/2, 1)`

• decreasing in `(1/2, 2)`

• increasing in `(−1, −1/2)`

• decreasing in `(−1/2, 1/2)`

Answer 1

The function f(x) = xe^{x(1 − x)}, x ∈ R, is `bbunderline ("increasing in" (−1/2, 1))`.

Explanation:

f(x) = xe^{x(1 − x)}

f'(x) = −ex(1 − x) (2x + 1) (x − 1) = 0

x = 1, `−1/2`

∴ f(x)is increasing in `(−1/2, 1)`