# Thread: Slope of tangent line

1. ## Slope of tangent line

Find the slopeof the functions graph at the given point.

f(x)= x / (x-2) point (3,3)

We have to use the method f(a+h)-f(a) / h to find the answers.
so I have it down to this and dont know what to do next so h will cancel.

((3+h)/(3+h-2) - 3) / h

2. just find the your derivative 1st

$\displaystyle \lim_{h \to 0} \frac{f(x+h) - f(x)}{h}$

which ends up being after you simplfy some.

$\displaystyle \lim_{h \to 0} \frac{-2}{x^2 - 4x -2h + xh +4}$

Do you know what to do next?

3. Originally Posted by 11rdc11
just find the your derivative 1st

$\displaystyle \lim_{h \to 0} \frac{f(x+h) - f(x)}{h}$

which ends up being after you simplfy some.

$\displaystyle \lim_{h \to 0} \frac{-2}{x^2 - 4x -2h + xh +4}$

Do you know what to do next?
ok backing up a step..how did you get from $\displaystyle \lim_{h \to 0} \frac{f(x+h) - f(x)}{h}$

to
$\displaystyle \lim_{h \to 0} \frac{-2}{x^2 - 4x -2h + xh +4}$

basically my problem is going from ((3+h)/ (3+h -2)) -3 / h to what you have. How did you simplify the numerator to get -2?

4. $\displaystyle \lim_{h \to 0}\frac{\frac{x+h}{x + h -2} -\frac{x}{x-2}}{h}$

$\displaystyle \lim_{h \to 0} \frac{\frac{(x+h)(x-2) -x(x+h-2)}{(x + h -2)(x-2)}}{h}$

$\displaystyle \lim_{h \to 0} \frac{(x+h)(x-2) -x(x+h-2)}{h(x + h -2)(x-2)}$

Can you take it from here?

5. Originally Posted by 11rdc11
$\displaystyle \lim_{h \to 0}\frac{\frac{x+h}{x + h -2} -\frac{x}{x-2}}{h}$

$\displaystyle \lim_{h \to 0} \frac{\frac{(x+h)(x-2) -x(x+h-2)}{(x + h -2)(x-2)}}{h}$

$\displaystyle \lim_{h \to 0} \frac{(x+h)(x-2) -x(x+h-2)}{h(x + h -2)(x-2)}$

Expand and add like terms after
Thank you so much. I understand how to do the problems, my simplification skills just aren't as up to date as I would like them to be. That helped me a lot thank you again.