Question

Find f(a), f(a+h), and the difference quotient f(a+h) - (fa)/h where h =/= 0.

Answer 1

What is f?

Answer 2

The function.

Answer 3

So what is your question :-D.

Answer 4

lol
you asked didn't you?

Answer 5

Oops forgot to put f(x) = 1/(x+1)

Answer 6

:-D

Answer 7

It is a derived

Answer 8

do you have an "a" as well or is it just "a"

Answer 9

It's just "a".
I'm getting \[((1/a+h+1)-(1/a+1))/h \] for f(a+h) - (fa)/h where h =/= 0 but that simplifies to no solution. I'm not sure if that's correct.

Answer 10

\[

\frac{f(x+h)-f(x)}{h}
= \frac{\frac{1}{1+x+h}-\frac{1}{1+x}}{h}
= \frac{1+x - (1+x+h)}{(1+x+h)(1+x)h}
= -\frac{1}{(1+x+h)(1+x)}

\]

Answer 11

it is correct so far but you need some algebra

Answer 12

ythemanifold cleared the fractions, then combined like terms in the numerator and canceled the h from top and bottom

Answer 13

also note that you should have -h in the numerator, which explains the "-" sign out front at the last step