Hello I Have a question about differance quotient

elcatracho

New member
Joined
Aug 9, 2005
Messages
25
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
 
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?
 
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)
 
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