Question

solve 3x^2-4x+1 using the limit definition of a derivative

Answer 1

Ok, do you know what the limit definition is?

Answer 2

ya

Answer 3

Alright, let's see what you got.

Answer 4

lim h->0 f(x+h)-f(x) / h

Answer 5

do you know how to plug your function into this?

Answer 6

no i forgot

Answer 7

So what you're going to want to do first is wherever there is an "x" in your function you'll place (x+h). Does that make sense?

Answer 8

ok so (3(x+h)^2-4(x+h)+1)/h

Answer 9

I think factoring might help us out first - on second thought.

Answer 10

Your post was f(x+h)/h. What you need to do is (f(x+h)-f(x))/h

Answer 11

ok my bad so ((3(x+h)^2-4(x+h)+1)-(3x^2-4x+1))/h

Answer 12

Maybe we should try factoring the function first however.

Answer 13

f=(3x-1)(x-1)

Answer 14

Meh nevermind that won't help

Answer 15

ok so ((3(x+h)-1)((x+h)-1))-((3x-1)(x-1))/h

Answer 16

Let's continue expanding your earlier equation

((3(x+h)^2-4(x+h)+1)-(3x^2-4x+1))/h

Answer 17

(3x^2+6xh+3h^2-4x-4h+1-3x^2+4x-1)/h

This would be the expansion

Answer 18

Do you see how I did this?

Answer 19

after that you get (3h^2-4h)/h

Answer 20

ya

Answer 21

I think your simplification is just a little off.

Answer 22

(3x^2+6xh+3h^2-4x-4h+1-3x^2+4x-1)/h

After the 3x^2, 4x, and 1 cancel.. you have

(6xh+3h^2-4h)/h

Answer 23

ok ya i see what i did wrong sorry running on fumes today

Answer 24

No problem.

Answer 25

Now all you need to do is cancel h's, take the limit, and you're good!

Answer 26

so so 6x-4

Answer 27

Correct.

Answer 28

ok thanks alot for the help

Answer 29

The key to using the limit definition to find the derivative is finding a way to be able to "cancel" the h on the bottom.

Answer 30

No problem!

Answer 31

ya i just forgot how to plug it into the equation

Answer 32

ok well i g2g to class thanks again

Answer 33

Gotcha. Glad I could help