Question

Consider a curve of the form
y(t) = at + b/t
with a local minimum at
(2, 8)

find a, and b.

I found the derivative to be a-(b/t^2) but i don't know the rest.

Answer 1

at local minimum: derivative =0

Answer 2

so set the derivative you found to zero, substitute 2,8

Answer 3

so would 't' be equal to 2?

Answer 4

as in [a-b/(2)^2 = 0?

Answer 5

yes

Answer 6

so a-b/4=0
thus
b=4a

Answer 7

now substitute (2,8) in your original equation: t=2 y=8

Answer 8

just to be sure, did you get a = 2 and b = 8?

Answer 9

Thank you!!!!

Answer 10

yep