Question

how do you solve this problem...
For f(x)=-3x^2+2x+1, find f(4+h)-f(4)/h. Simplfy completely

Answer 1

Substitute (4+h) and (4) into your function...

Answer 2

like -3(4+h)-(4)+2(4+h)(4)+1?

Answer 3

-3(4+h)+2(4+h)+1 - (-3(4)^2+2(4)+1) /h Do yu see what I did?

Answer 4

yeah i think so.

Answer 5

but you don't write the first as -3(4+h)^2+2(4+h)+1? and why did you subtract them?

Answer 6

Yes I made and error on the first part. You subtract them because you orginal equation f(4+h)-f(4). Understand.

Answer 7

oh i see now.

Answer 8

Now you need to expand your equation.

Answer 9

so i would distribute them?

Answer 10

Yes..be very careful when doing this as you must always remember that you are subtracting the whole equation. That is why I always place it in brackets and show it above as. Fist part of the equation..- (-3(4)^2+2(4)+1)...

Answer 11

ok am I on the right track?
-3(16+8h+h^2)+8+2h+1

Answer 12

Yes distribute the -3

Answer 13

ok would it be.... -39-22h-3h^2

Answer 14

-48-24h-3h^2..now do the other part

Answer 15

but what do you do with the 8+2h+1?

Answer 16

Oh..my bad you combined terms..you are correct..

Answer 17

ha yeah. Ok so is this all i do for this part of the problem?

Answer 18

Yes..but you have to subtract the other part then divide the whole thing by h.

Answer 19

okay so the other part other the problem i got a -22
so....-39-22h-3h^2-(-22)
It's gonna become a plus sign?

Answer 20

Not -22 might check that again

Answer 21

oh ok so it's -39?

Answer 22

Yes and you are right it will become positive. So what do you end up with?

Answer 23

-22h-3h^2/h

Answer 24

Which simplifies to what?

Answer 25

22-3h?

Answer 26

-22-3h?

Answer 27

Very good...This is the difference equation you will see it many times in pre calculus...Do it few times and it becomes easy...Great job..

Answer 28

oh okay ha thanks. Now how do I check if thats the solution?

Answer 29

You would have to do it a second tome and see if you get the same result

Answer 30

What do you mean? Just redo the problem?

Answer 31

Yes

Answer 32

there isnt another way? like plugging in what we got into the equation?

Answer 33

Hold on

Answer 34

ok

Answer 35

Nope no way to check the answer in that this is a formula with h as a variable. And it is called the "Difference Quotient"

Answer 36

ha ok I hope my teacher accepts that. thanks for your help

Answer 37

Anytime