# Slope of funtions graph

1. Jun 1, 2014

### TommG

I have to find the slope of the function

g(x) = x/(x-2), (3,3)

my attempt

[(3+h)/((3+h)-2)] - [(3)/(3-2)] $\div$ h

got rid of (3+h) and 3
[(1/-2) -(1/-2)] $\div$ h
0/h

Last edited: Jun 1, 2014
2. Jun 1, 2014

$g(x)=\frac{x}{x-2}$ right?
Can't you use the quotient rule?

3. Jun 1, 2014

### TommG

yes g(x)= x/(x-2)

I don't think I can use the quotient rule. Don't you need a limit? I wasn't given a limit only a function.

4. Jun 1, 2014

No.
You can solve it in two ways.
1. The definition of the derivative of a function
2. Quotient rule
The definition of the derivative of a function $f$ with respect to x: $\frac{\text{d}f}{\text{d}x}=\lim_{\Delta x \to 0}\frac{f(x+\Delta x)-f(x)}{\Delta x}$

The quotient rule states that $(\frac{u}{v})'=\frac{u'v-uv'}{v^2}$ Where u is the numerator and v is the denominator.

The quotient rule is much easier.

5. Jun 1, 2014

### verty

${x \over x-2} \not = {1 \over -2}$.

You may want to review fractions and what manipulations are allowed.

6. Jun 1, 2014

### TommG

Ok then I have to use the first option. Not allowed to use the second option yet.

this is the definition I have to use

The definition of the derivative of a function $f$ with respect to x: $\frac{\text{d}f}{\text{d}x}=\lim_{h \to 0}\frac{f(x+h)-f(x)}{h}$

7. Jun 1, 2014

Your attempt:$$\frac{\frac{3+h}{(3+h)-2}-\frac{3}{3-2}}{h}$$ is correct.
You only have some algebra problems in simplifying that. Try again.

If you use that definition,you will get the derivative with respect to x. If you use 3 instead of x, you will get derivative of the function at x=3. That's what you did there in your attempt

Last edited: Jun 1, 2014
8. Jun 1, 2014

### TommG

thank all of you who helped I have figured it out. I do not need help anymore.

9. Jun 1, 2014