Question

The function g(x) = `(f(x))/x`, x ≠ 0 has an extreme value when ______.

Options

• g'(x) = f(x)

• f(x) = 0

• xg'(x) = f(x)

• g(x) = f'(x)

Answer 1

The function g(x) = `(f(x))/x`, x ≠ 0 has an extreme value when g(x) = f'(x).

Explanation:

g'(x) = `(xf^'(x) - f(x))/x^2`

= `(x[f^'(x) - g(x)])/x^2` = 0

⇒ f'(x) = g(x)