Question

Extreme values of f(x) = ln(x+1) if 0≤x≤3?

Answer 1

The function is f(x) = ln(x + 1) and the interval is [0, 3].

Apply first derivative with respect to x.

f'(x) = 1/(x + 1)

To find the critical or key numbers, to make the first derivative equal to zero [ f'(x) = 0] or f'(x) does not exist.

f'(x) does not exist when x+1 = 0 ⇒ x = -1.

The critical x = -1 does not lie on the interval [0, 3].

Left-end point: x = 0 ⇒ f(0) = ln(0 + 1) = 0 (Minimum)

Right-end point: x = 3 ⇒ f(3) = ln(3 + 1) = 1.386 (Maximum)