Question

Let f(t)=4 t^2 + 4/t^2. Find the slope of the curve at t = -3.

Answer 1

f(t)'=8t -(8)/t^3 for t=-3
-24-8/27
-640/27=-20

Answer 2

Ooop it is not -20 -640/27=-23.7037

Answer 3

yeah I got df/dt=8t-2/t^2 so t=-3 => 8*(-3)-2/(-3)^2 -24-2/9 ! but i dont trust my work

Answer 4

the second term when you differentiated;\[4 \over t ^{2}\]is\[4 t ^{-2}\]becomes \[-8 t ^{-3}\]

Answer 5

or\[-8\over t ^{3}\]

Answer 6

but I would still have to plug in -3 for t

Answer 7

Yes indeed.

Answer 8

wait was I on the right track to getting the answer?

Answer 9

that would be -8/27 for that term and 24 for the first term I see what you mean it can't be negative with 24 being positive!! lol, I better take a nap.

Answer 10

but -640/27=-23.7037 is the answer

Answer 11

right?

Answer 12

Oh yes, thats right as t=-3 so it would be -24 and a negative 8/27 that means we have to combine the -24 and the -8/27 giving -648/27 - 8/27=-656/27= -24.29

Answer 13

Looking at your next to last post. How did you get -640/27? Wouldn't -24 X 27 =-648 ??

Answer 14

It would appear so, if I have kept track of the signs.

Answer 15

But maybe I messed up let me think about this?

Answer 16

lol take your time

Answer 17

I think I did mess up on that 2nd term when I plugged in the minus 3\[-8\over t ^{3}\]\[-8\over (-3)^{3}\]\[-8\over -27\] or POSITIVE 8/27 lol there it is.

Answer 18

So we ADD the 8/27 to the negative 648/27 giving -640/27
So sorry paunic88, I did stray off the path of keeping track of signs.

Answer 19

ok so the final anwser is -640/27 right? (ill compute it later)

Answer 20

-3 X -3 X -3 = -27 lol

Answer 21

Yes.

Answer 22

Good luck with your studies,and don't err with signs lol

Answer 23

ok thank you very much for the help

Answer 24

ur welcome.