Question

Find the difference quotient and simplify your answer.

f(x) = x^2 - x + 1, f(5+h)-f(5)/h, h can not = 0

Answer 1

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

Answer 2

Simplify that on its own first.

Answer 3

Expand it.

Answer 4

Expand it? I'm sorry I'm really horrible at math.
So basically just multiply it out like...
\[5f+hf=25+10h+h^2-(5+h)+1?\]

Answer 5

yeah \[
25+10h+h^2-5-h+1=h^2+9h+21
\]

Answer 6

Ah, okay. That's it?

Answer 7

Now what is \(f(5)\)?

Answer 8

Wouldn't you replace f with 5? But in the equation you posted there's no f :/

Answer 9

replace \(x\) with \(5\).

Answer 10

oH x, that's what i meant, not f.
but there's still no x in the equation you posted unless you mean replace the h?
or are you telling me to do
\[f(5)=x^2-x+1\] ?

Answer 11

Yes.

Answer 12

Replace x or the h? which did you say yes to? sorry :c

Answer 13

Okay so far we already calculated \(f(5+h)\).
Now we need to calculate \(f(5)\)

Answer 14

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

Answer 15

Okay. So, \[f(5)=25-5+1 \] which is \[f(5) = 21\] ?

Answer 16

Yes.
Now we can put then both into : \[
\frac{f(5+h)-f(5)}{h}
\]

Answer 17

Ah so it would be \[(h^2+9h+21)-(21) / h ?\] and then... \[h^2+9h / h\] ?

Answer 18

Yeah, now simplify.

Answer 19

\[h+9\] ?

Answer 20

In my book it says the answer should be \[3+h, h \neq 0\] how does it get to be 3?

Answer 21

I'm not sure...

Answer 22

http://www.wolframalpha.com/input/?i=%5B%285%2Bh%29%5E2-%285%2Bh%29%2B1+-+%285%5E2-5%2B1%29%5D+%2Fh

Our answer is correct.

So their answer is wrong or our function is wrong.

Answer 23

Ah, it must be a mistake because my friend had the same answer as well.
Thank you so much!