Question

Given the following table of values determine the value of X where f(x) has a local minimum. Assume that f is continuous and differentiable for all reals

Answer 1

We have to find the value of x for which f(x) has a minimum.

Extreme values of f(x), like minimum or maximum values, correspond to values of its derivative equal to 0.

In this case f'(x) = 0 for x = -2 and x = 0.

We can find if this extreme value is a minimum if the second derivative f''(x) is greater than 0.

In this case, f'(x) = 0 and f''(x) > 1 for x = 0.

Then, x = 0 is a local minimum.

Answer: x = 0