Calculate (f(w) - f(x)) / (w-x) for f(x) = 3x2-5

[Loppyfoot]

Homework Statement

Find (f(w) - f(x)) / (w-x)
and
(f(x+h) - f(x)) / (h)
Simplify as much as possible. This section is a functions section, so I cannot take the derivative.

Homework Equations

f(x) = 3x²-5

The Attempt at a Solution

What is the w and the x? Also, what is the h? I have no idea where to begin. Thanks for your help.

 

[snipez90]

They are just variables that can really be substituted with any other letter. These are normally two ways of expressing the difference quotient in differential calculus. In this case, they usually represent average rate of change but all you have to do is plug in the appropriate variables into the function you are given.

 

[jgens]

In this case $h = \Delta{x}$ and $w$ is some value in the function's domain. Hopefully you know what the $x$ is there for. :)

 

[n!kofeyn]

The x, w, and h are just variables. In this case, they can be any real number, so we just represent them with letters. For example f(w)=3w²-5. The f is a function so it takes an input and gives an output based upon the input. You could write it as f(input)=3(input)²-5=output. Now you should be able to do the first one. For the second one, what does f(x+h) equal?

Also, you should recognize that these formulas are the same thing really. Let w=x+h (or h=w-x) and convince yourself of this fact.

 

[Loppyfoot]

The answers that are supplied in the back of the textbook are 6x+3h, and 3w+3x.

I am in no way getting these when I work them out. I need some guidance. Thanks...

 

[n!kofeyn]

It's just algebra! I already told you what f(w) is. I'll do part of the first one for you.
$$\frac{f(w)-f(x)}{w-x}=\frac{(3w^2-5)-(3x^2-5)}{w-x}=\frac{3w^2-5-3x^2+5}{w-x}=\frac{3(w^2-x^2)}{w-x}$$
Now finish it using the difference of two squares.

For the second one, what is f(x+h)? I asked this in the last post, and you didn't give an answer. It is best on this forum to attempt to show what work you have done, otherwise people get the feeling you want them to do your homework for them. So please post what work you do if you get stuck again, not what the answers are in the back of the book. :)