Question

Find the exact location of all the relative and absolute extrema of the function. Question attached

Answer 1

So, you want to find all of the t-values for which your derivative is 0 and also include the endpoints created by your restriction.

Answer 2

I believe so

Answer 3

h'(t) = 51t^2 - 102t = 0 at local turning points
51t(t - 2) = 0
t = 0 and t = 2
- local max/min at these points
h"(t) = 102t - 102 which negative if t=0 and positive for t = 2

so local maximum at (0,0) and local minimum at (2,-78)

Answer 4

* you also have to test the endpoint from the restriction t>= -1