Question

Suppose u′(t)=(t−1)(t−4)(t−8) . Find the point in the interval [1,8] for which the function u(t) takes its maximum.

Answer 1

first find the second derivative which would give you the equation that determines concavity. Set u'(t) = 0 and solve for (t = 1 ,4 and 8) and then check using u''(t) to see if concavity switches between those points.

Answer 2

or look at the sign changes of \(u'\)

Answer 3

at \(1\) you know \(u'\) goes from negative to positive, making \(1\) a local min

Answer 4

Oh you are right, idk why I had to overcomplicate things like that...