Expert: Paul Klarreich - 1/22/2007

Question
i need some help with this problem

the question is:
evaluate the difference quotient for the given function.Simplify your answer.

F(x)= (1/x),  (f(x)-f(a)/h)

I do the substitution on the function and i get: -1/(xa)

i need to know how did i get this.

Answer
Questioner:   israel
Category:  Calculus
 
Subject:  Calculus I
Question:  i need some help with this problem

the question is:
evaluate the difference quotient for the given function.Simplify your answer.

F(x)= (1/x),  (f(x)-f(a)/h)

I do the substitution on the function and i get: -1/(xa)

i need to know how did i get this.
..........................................
Hi, Izzy,

(well, that's what we call all our friends who have that name)
 
There is more than one form of the difference quotient.  
   f(x + h) - f(x)
A.  ---------------
          h

  f(x) - f(a)
B. ------------
    x - a

Use one or the other, but not both at the same time.  For your F(x) = 1/x,

   f(x + h) - f(x)
A.  --------------- =
          h
   1       1
------- - ---
(x + h)    x
--------------- =
       h

   x  - (x + h)
----------------
    x(x + h)
--------------- =
       h

     - h
------------- =
   hx(x + h)

     - 1
------------- =
   x(x + h)

That's as far as you can go, and it's the answer if you use this form.


  f(x) - f(a)
B. ------------ =
    x - a

 1     1
--- - ---
 x     a
---------- =
 x - a

 a - x
-------
   ax
---------- =
 x - a

-1(x - a)
--------- =
ax(x - a)

 -1
-----
 ax

So you did fine.  As to how YOU got it, I wasn't there, so I can't tell you.