# Thread: Slopes of a Polynomial Function

1. ## Slopes of a Polynomial Function

g'(x)=lim (g(x+h)-g(x))/h The limit is h>0
This is the equation I got for slope.

The actual problem is g(x)=2/(x-2) and I am asked to use the Difference Quotient and g(x) to find the slope.

Evaluate g(x + h):

. . . . .$\displaystyle g(x\, +\, h)\, =\, \frac{2}{(x\, +\, h)\, -\, 2}$

Subtract g(x) from this:

. . . . .$\displaystyle \frac{2}{x\, +\,h\, -\, 2}\, -\, \frac{2}{x\, -\, 2}$

Convert to a common denominator:

. . . . .$\displaystyle \frac{2(x\, -\, 2)\, -\, 2(x\, +\, h\, -\, 2)}{(x\, -\, 2)(x\, +\, h\, -\, 2)}$

. . . . .$\displaystyle \frac{2x\, -\, 4\, -\, 2x\, -\, 2h\, +\, 4}{(x\, -\, 2)(x\, +\, h\, -\, 2)}$

. . . . .$\displaystyle \frac{-2h}{(x\, -\, 2)(x\, +\, h\, -\, 2)}$

Then you divide by h. Where are you stuck?