Hello I Have a question about differance quotient

[elcatracho]

I've always had trouble with this type of problem and i've been thinking about how to solve it but i'm unsure of how to do it or set it up. The question is..
f(x)= 1/x Find: (f(x+h)-f(x))/(h) I would really be thankful for some assitance on this problem. Thanks, Luis

 

[Gene]

Don't let them throw you. When they mention f(?) replace the x in f(x) with the ?
f(x+h) = 1/(x+h)
f(x) = 1/x so
(f(x+h)-f(x))/(h) =
(1/(x+h) - 1/x))/h
Is that enough of a hint?

 

[soroban]

Hello, Luis!

Here's my baby-talk approach . . .

Given: f(x) = 1/x

Find: [f(x+h) - f(x)]/(h)

Think of the Difference Quotient as a "three step recipe":
. . (1) Find f(x + h) . . . replace x with x+h (and simplify)
. . (2) Subtract f(x) . . . the original function (and simplify)
. . (3) Divide by h . . . . factor and cancel

. . . . . . . . . . . . . . . . . . . . . . . . 1
(1) Find f(x + h): . f(x+h) .= .-------
. . . . . . . . . . . . . . . . . . . . . . .x + h

. . . . . . . . . . . . . . . . .1 . . . 1 . . . . .x - (x + h) . . . . . .- h
(2) Subtract f(x): . ------- - --- . = . ------------- . = . ----------
. . . . . . . . . . . . . . . x + h . .x . . . . . x(x + h) . . . . . x(x + h)

. . . . . . . . . . . . . . 1 . . . - h . . . . . . . . - 1
(3) Divide by h: . --- . ---------- . = . ----------- . . . . . There!
. . . . . . . . . . . . . . h . .x(x + h) . . . . x(x + h)