If f(x) is a differentiable function on the domain [-2,7] and of its only critical number is a=3, at which locations can the absolute maximum this function has only occur? Click all possibilities.

Question

Answer choices:

1. -2
2. 0
3. 3
4. 7
5. no conclusion possible

Answer 1

Absolute max of a continuous function defined on a closed interval can occur only at a critical number in the interval or at an endpoint of the interval.

Note: since the function is differentiable, it is automatically continuous

So, absolute max can occur only at x = -2, 3, or 7