Question

The position of an object at time t is given by s(t) = -8 - 9t. Find the instantaneous velocity at t = 1 by finding the derivative.

Answer 1

what is the derivative?

Answer 2

@emersonba123 ?

Answer 3

That's all that the problem gave me. Do you need the equation? f(x+h)-f(x)/h

Answer 4

yes

Answer 5

do that and tell me what you get

Answer 6

Do I substitute s(t) for f(x)?

Answer 7

yep

Answer 8

(-8 - 9(t+h)-(-8 - 9t))/h

Answer 9

simplify and run the limit and tell me what you have

Answer 10

I got -8

Answer 11

should be -9

Answer 12

isn't this just taking the derivative of s(t)

Answer 13

yes they don't know the shortcut rules yet

Answer 14

so from the deffinition

Answer 15

really? I am sure they have seen the power rule at this point

Answer 16

are you in the class?

Answer 17

This is exactly the sort of problem they give you with the definition.

Answer 18

(-8 - 9(t+h)-(-8 - 9t))/h = (-8-9t-9h+8+9t)/h = -9h/h = -9

Answer 19

Okay guys. Pause. When I distribute, I get (-8-9t-9h+8+9t)/h and the -9t and +9t would cancel out and leave you with -8-9h+8/h

Answer 20

so your derivative function is f(x) = -9

Answer 21

and the 8's cancel out. Okay, I see it now.

Answer 22

so what is f(1) = -9

Answer 23

Wouldn't it just be -9 since there are no x's

Answer 24

yes

Answer 25

yay! Thank you so much!

Answer 26

np

Answer 27

in about 1 week you will be able to answer this problem without doing anything, just by looking at it

Answer 28

they will teach you a "trick" no more f(x+h).....

Answer 29

d/dx cx^n = ncx^(n-1)
Best rule ever!

Answer 30

don't use it though, until your teacher tells you the rule.

Answer 31

great for checking work though:)

Answer 32

No just use it right away. Your teacher will be impressed and let you test out of the class

Answer 33

lol

Answer 34

also tell your teacher what he calls a linear function is actually an affine function, they will love you

Answer 35

I have no idea what any of that is..

Answer 36

ignore us @emersonba123