Question

Suppose f(t)=3t^3+5t^2+3t-5 . Find the value of t in the interval [4,8] where f(t) takes on its minimum.
What I have so far is only the derivative f'(t)=9t^2+10t+3

Answer 1

set it equal to zero and solve
then check the zeros and also the endpoints of the interval

Answer 2

actually, scratch that, this one has no zeros, it is always positive
that means your function is always increasing
so the minimum occurs at the left hand endpoint and the maximum occurs at the right hand endpoint

Answer 3

@satellite73 what do you mean by left and right hand endpoint?

Answer 4

Find the value of t in the interval [4,8] where f(t) takes on its minimum.

Answer 5

\(4\) is the left endpoint of the interval, \(8\) is the right

Answer 6

So you would plug in 4 and 8 in the equation or set it equal to?

Answer 7

actually to be literal and just answer the question
Find the value of t in the interval [4,8]
the answer would be \(4\)

Answer 8

it doesn't actually ask for the minimum, just the value of \(t\) that gives it

Answer 9

Ah okay! Thank you!