Question

Consider a curve of the form
y(t) = at + (b/t), with a local minimum at
(3, 12).


(c) find the exact values of a and b that satisfy the conditions in part (a).
--> part a: (3,12) tells us that y(3)=12

Answer 1

My professor did not go over this in class so I need to see how this problem is done; I have three other problems on my homework like this problem.

Answer 2

Alright, so this seems doable.
So the problem tells us that this function has a local minimum at (3,12).
How do we find the local minimum of a function?

Answer 3

You find the 1st derivative of the function, set it equal to zero, and do the first derivative test to see whether its a min or max right..?

Answer 4

Good. And what would the derivative of this function be?

Answer 5

a-(b/t^2)..?

Answer 6

Correct.

Answer 7

Now at a local minimum the derivative equals 0, right?

Answer 8

so how would i find the values of a and b though? :/

Answer 9

yeah!

Answer 10

What we're working towards right now is getting two equations that relate a and b.
Then we can use those equations to solve for a and b.