Expert: Sherry Wallin - 11/23/2009

Question
I have a question on solving a function equation, its very simple it just gets me confused every time.
this is the question:

Given: f(x)=x^2+4x, find f(x+h)-f(x)/h  

Answer
Rene~
    There are a number of ways to do this. One way is to put into English what the rules of the function are: This says that whatever you put into the function you want to square it and add 4 times it to the square of it. So take (x+h) square it: x^2 +2xh + h^2; multiply (x+h) by 4: 4x + 4h and add that to your previous total: x^2+2xh+h^2 +4x + 4h and  subtract off x^2+4x: x^2+2xh+h^2+4x+4h-x^2-4x
= 2xh+4h+h^2. Next divide this result by h (factor out an h on top first) h(2x+4+h)/h = 2x+4+h  

When you type in a problem it is important to type it in correctly using parenthesis:
find f(x+h)-f(x)/h is incorrect, type it in as [f(x+h)-f(x)]/h. The h divides both terms and the way you have it written it is only dividing the 2nd term, i.e., h is only dividing the f(x).

Math Prof