Question

Suppose u'(t)=(t-1)(t-6)(t-8) . Find the point in the interval [1,8] for which the function u(t) takes its maximum.
How do I go about finding the answer?

Answer 1

You have the derivative. The slope is zero when it reaches an extrema. In order to find a local maxima, you must evaluate the function between a given interval (basic subtraction). Can you go from there?

Answer 2

so set it to zero?

Answer 3

Yes.

Answer 4

Then, solve for t.