find the absolute maximum and absolute minimum

Question

Using calculus, find the absolute maximum and absolute minimum of the function fx=7x2−42x+2 on the interval [−4,4]

absolute maximum?

 

  

absolute minimum?

Answer 1

The absolute extrema of a continuous function that is defined on a closed interval occur either at a critical number in the interval or at an endpoint.

f'(x) = 14x - 42 = 0 when x = 3

Check f(3), f(4), and f(-4). The largest of these three values is the absolute max and the smallest is the absolute min.