Question

Find the difference quotient of f, that is find (f(x+h) - f(x))/ (h) for the function f(x)= x^2 + 5x - 1

Answer 1

at what point are you stuck?

Answer 2

I just really don't understand what the question is asking and what I am supposed to do. Do you want me to rewrite the equation to make it look better?

Answer 3

no I understand it fine thanks :)
what is f(x+h) ?
to find it, just replace every x in f(x) with x+h
what do you get?

Answer 4

\[f(x) = x ^{2} + 2xh +h ^{2} + 5h + 5x -1\]

Answer 5

yes :)
so what is f(x+h)-f(x)?

Answer 6

@Brybro where did u get the 5h?

Answer 7

So do I just take that equation I just posted and subtract from the original f(x) equation right?

Answer 8

would it be.... x^2+2xh+h^2+4x-1?

Answer 9

right

Answer 10

@dsrnation no

Answer 11

@dsrnation give me a sec. I will post my work soon

Answer 12

@TuringTest can you check my answer after im done?

Answer 13

sure thing

Answer 14

\[f(x) = h ^{2} + 2xh + 10x + 5h - 2\]

Answer 15

careful what you write, that is not f(x) but rather f(x+h)-f(x)

Answer 16

actually it's wrong anyway :P

Answer 17

x^2+2xh+h^2=4x=3h-1?

Answer 18

meant for the = tp be +

Answer 19

\[f(x+h)=x^2+2xh+h^2+5x+5h-1\]\[f(x)=x^2+5x-1\]\[f(x+h)-f(x)=x^2+2xh+h^2+5x+5h-1-(x^2+5x-1)\]

Answer 20

\[f(x+h)-f(x)=2xh+h^2+5h\]

Answer 21

Oh i forgot to distribute the - sign. That makes since

Answer 22

yep, so now the only thing missing is the "over h"
so divide this all by h and that is the difference quotient

Answer 23

i know this isnt my problem but thanks!!! i just started learning these!

Answer 24

no prob :)

Answer 25

So the answer is 2x + h + 5?

Answer 26

yes, nice job

Answer 27

Thanks so much. I have a test tomorrow and I'm not the best at math. Think you could hel me with one more question for now?

Answer 28

I'm a bit busy, but post it separately and I'll help as much as I can

Answer 29

No problem. Thanks