Expert: Paul Klarreich - 3/23/2008

Question
Q1.find the Difference Quotient f(x+h)-f(x)/h and simplify the result
A) f(x)=1/x
B) f(x)=1/radical x

Answer
Questioner:   Ghous Khan
Category:  Calculus
Private:  No
 
Subject:  Functions
Question:  Q1.find the Difference Quotient f(x+h)-f(x)/h and simplify the result
A) f(x)=1/x
B) f(x)=1/radical x
...........................
Hi, Ghous,

Since you didn't indicate what you already tried to do on these, I can't tell what went wrong, and I will assume you only need to get started.
    f(x + h) - f(x)
DQ = ---------------
          h

A) f(x) = 1/x

    1/(x + h) - 1/x
DQ = ---------------  << clue: ALWAYS PARENTHESIZE.
          h
From here on, you simplify.  First clear fractions using x(x + h) as the common denominator.  You should reach a point where some h will cancel.  If you don't, you messed up the algebra. [Probably because you did not parenthesize properly.]

B) f(x) = 1/sqrt(x)  << that's how to write it.

    sqrt(x + h) - sqrt(x)
DQ = ---------------------
            h

From here on, you simplify.  First rationalize using
(sqrt(x + h) - sqrt(x)) as the rationalizing factor.  You should reach a point where some h will cancel.  If you don't, you messed up the algebra. [Probably because you did not parenthesize properly.]