Question

PLEASE HELP A GIRL OUT

The position of an object at time t is given by s(t) = -1 - 13t. Find the instantaneous velocity at t = 8 by finding the derivative.

Answer 1

take the derivative using the power rule and then sub 8 for t

Answer 2

s ' (8) is what you are looking for

Answer 3

Okay but how do I write that out?

Answer 4

do you know the power rule? It is the most basic rule for taking derivatives in calculus. It is the easiest one of all.

Answer 5

y=3x^2
y ' = 6x

Answer 6

http://www.mathsisfun.com/calculus/derivatives-rules.html

Answer 7

oh okay. why did you use those numbers though?

Answer 8

just to give you an example of power rule
y = x^2
y ' = 2x

Answer 9

Okay, but how do I find what x is?

Answer 10

for your solution you take the derivative
ie s ' (t) and then sub 8 for t

Answer 11

example
f(x) = x^2 and I want f ' (3)
then
f ' (x) = 2x
f '(3) = 2(3)
f'(3)=6

Answer 12

do you see what your solution is?

Answer 13

s′(t)=−13

Answer 14

right?

Answer 15

yes and guess what
s ' (8)=-13 also, only because you don't have a variable to sub into

Answer 16

wait so this s ' (8)=-13 is all? There aren't any other steps?

Answer 17

@precal

Answer 18

no because we don't have a variable to sub into

Answer 19

so I can just write:

s ' (t)=−13
s ' (8)=-13

or do I need to write it differently? @precal

Answer 20

the first one represents the first derivative of your function
the second one represents the derivative at that particular time in this case t=8

Answer 21

go with the second one
the first one is the velocity
the second one is the velocity at that given time

Answer 22

Thanks :)

Answer 23

yw