1. ## Rational function

What do you mean by this?

Find $\displaystyle \frac{f(x+h)-f(x)}{h}$ for:

$\displaystyle f(x)=3x^2-4x+1$

Can you explain me what is this problem? thanks!

2. Originally Posted by Anemori
What do you mean by this?

Find $\displaystyle \frac{f(x+h)-f(x)}{h}$ for:

$\displaystyle f(x)=3x^2-4x+1$

Can you explain me what is this problem? thanks!
Hi

In this case

$\displaystyle \frac{f(x+h)-f(x)}{h} = \frac{(3(x+h)^2-4(x+h)+1)-(3x^2-4x+1)}{h}$

Expand and simplify

3. Originally Posted by running-gag
Hi

In this case

$\displaystyle \frac{f(x+h)-f(x)}{h} = \frac{(3(x+h)^2-4(x+h)+1)-(3x^2-4x+1)}{h}$

Expand and simplify

This is what i get:

6x+3h-4

now my problem is how to graph f(x) and its difference quotient in same window..... hmmm.....

pls help,,, thanks!

4. Originally Posted by Anemori
This is what i get:

6x+3h-4
That is correct

Originally Posted by Anemori
now my problem is how to graph f(x) and its difference quotient in same window..... hmmm.....
You cannot graph the difference quotient unless you give a value to h (otherwise you have 2 variables : x and h)

Usually when you have to compute $\displaystyle \frac{f(x+h)-f(x)}{h}$ you make h go to 0 (as an introduction to the derivatives), which gives 6x-4

5. Originally Posted by running-gag
That is correct

You cannot graph the difference quotient unless you give a value to h (otherwise you have 2 variables : x and h)

Usually when you have to compute $\displaystyle \frac{f(x+h)-f(x)}{h}$ you make h go to 0 (as an introduction to the derivatives), which gives 6x-4

Here is the instruction for graphing it:

Graph f(x) and its difference quotient by hand in the same window. Provide all relevant work regarding the vertex, axis symmetry, etc.

True or false? The root of difference quotient when h=0 is the x-coordinate of the minimum of f(x).

I guess it says i have to graph it with h=0.