At what value of does the local max of occur?
Please help!
At a local max of f(t), f'(t) must = 0. By the fundamental theorem, you can get f'(t) by replacing x with t in the integrand.
f'(t) = 0. So, $\displaystyle x^2 + 14x +24 = 0$.
Solving that equation will give you the critical points where a max is possible.