Question

consider the function f(x)=5x^2-17x+6
1. find f(x+h)

Answer 1

just plug in "x+h" for "x" expand and/or simplify as necessary

Answer 2

5*(x+h)^2 -17(x+h) +6

Answer 3

= 5*(x^2+ 2*x*h+ h^2) -17*(x+h) +6 and so on....

Answer 4

Thank you

Answer 5

sure:) that help? was there more to the problem?

Answer 6

yes for number 2 of the problem it says for h cannot equal 0, find f(x+h)-f(x)/h

Answer 7

yep, I thought so:)

Answer 8

so we found f(x+h) now let's add f(x) to it and simplify...

Answer 9

-f(x) I meant ...

Answer 10

5*(x^2+ 2*x*h+ h^2) -17*(x+h) +6 - ( 5x^2-17x+6 )

Answer 11

notice the 5*x^2 's cancel.... what else?

Answer 12

well just real quick, sorry. how did you get the -f(x) ?

Answer 13

just made the entirety of f(x) negative... (ie I put a minus sign in front of f(x) )

Answer 14

- ( 5x^2-17x+6 )

Answer 15

so -5*x^2 +17*x -6

Answer 16

oh, okay yest! i see it.

Answer 17

so simplify the rest and let me know what you get...

Answer 18

okay

Answer 19

so i got 2xh+h^2+17h. would i need to further break that down?

Answer 20

does it just stay in that format?

Answer 21

well remember, it was all over 'h' (we left that out while we were simplifying the numerator...)

Answer 22

so there's one more simplification to make... factor the h out of the numerator and h/h =1

Answer 23

looks like you forgot to multiply a few terms by the '5' too... go back and fix that...

Answer 24

2xh+h^2-85x-85h+30+17x-6/h can you tell me if so far i'm on the right path?

Answer 25

you're skipping steps or something

Answer 26

5*(x^2+ 2*x*h+ h^2) -17*(x+h) +6 - ( 5x^2-17x+6 )

Answer 27

do the first term on the left 5*(x^2+ 2*x*h+ h^2) = ?

Answer 28

5x^2+10xh+5h^2 ?

Answer 29

good:)

Answer 30

rest is pretty easy

Answer 31

-17x -17h +6 -5x^2 +17x -6

Answer 32

17x and 17x cancel 6 and -6 cancel all that's left is -17h and -5x^2

Answer 33

what you got from the first step : what I got from the 2nd:
5x^2+10xh+5h^2 -17h -5x^2

Answer 34

Is that the format I would leave it in? I wouldn't need to further break it down?

Answer 35

combine and you get 5h^2 +10xh -17h

Answer 36

then we need to put that all over h:
(5h^2 +10xh -17h)/h = 5h +10x-17

Answer 37

Thank you so much. For some reason I was having such a stressful time with this problem and I kept coming up with answers that made no sense.

Answer 38

:) hope it helped!

Answer 39

it really did. thank you!

Answer 40

sure!