Expert: Paul Klarreich - 1/21/2008

Question
I need step by step directions on how to solve this:
Find f(x+h)-f(x)/h if f(x)=7x(squared) +5x-14.

Please help

Answer
Questioner:   Bonnie
Category:  Advanced Math
Private:  No
 
Subject:  Help solving functions
Question:  I need step by step directions on how to solve this:
Find f(x+h)-f(x)/h if f(x)=7x(squared) +5x-14.

Please help
..........................................
Hi, Bonnie,

You are not SOLVING this -- it isn't an equation.  If you use the vocabulary carelessly, you lose understanding.  Be very careful about the vocabulary; know what the words mean and use them right -- you'll cut down on your misunderstandings.

This is just a matter of doing the operations indicated.

IF f(x) = x^2 + 5x - 4, then

f(x + h) MEANS substitute x+h for x.  Do it this way:

Rewrite the function, putting empty parentheses wherever you see x:

f( ) = ( )^2 + 5( ) - 4

Put your 'argument' into the ():

f(x + h) = (x + h)^2 + 5(x + h) - 4

Do some algebra, like removing parentheses.

f(x + h) = x^2 + 2hx + h^2 + 5x + 5h - 4

Now write  f(x):

f(x) = x^2 + 5x - 4

Now subtract to get  f(x + h) - f(x).  Do it right! Use parentheses:

f(x + h) - f(x) = x^2 + 2hx + h^2 + 5x + 5h - 4 - (x^2 + 5x - 4)

Do some more algebra, like removing parentheses.

f(x + h) - f(x) = x^2 + 2hx + h^2 + 5x + 5h - 4 - x^2 - 5x + 4

Do obvious simplifications.

f(x + h) - f(x) = *** + 2hx + h^2 **** + 5h *** - *** **** ***

f(x + h) - f(x) = 2hx + h^2 + 5h

Now divide by h, as it says in

f(x + h) - f(x)   2hx + h^2 + 5h
--------------- = -----------------
     h                h

f(x + h) - f(x)   h(2x + h + 5)
--------------- = -------------
     h                h

f(x + h) - f(x)   
--------------- = 2x + h + 5
     h               
That's it.