Question

how can i apply the difference quotient to this funtion: g(x)=(x)/(x-2) at (3,3)

Answer 1

u didn't check ur previous post?

Answer 2

yes i did but, i would like to solve it using this formula: lim as x goes to 0, of (f(x+h)-(f(x))/(h)

Answer 3

differentiation by definition

Answer 4

what does that mean?

Answer 5

this is what u want :),

Answer 6

\[g'={{{x+h} \over{x-2+h}}-{{x} \over{x-2}} \over h}\]

Answer 7

=(x+h)(x-2)-x(x-2+h)/(x-2+h)(x-2)h

Answer 8

The top part gets cross multiplied

Answer 9

by taking the lcm

Answer 10

x^2+hx-2x-2h-x^2+2x-hx/(x-2+h)(x-2)h
=-2h/(x-2+h)(x-2)h
=-2/(x-2+h)(x-2)
=-2/(x-2)^2 in the loim h ---->0

Answer 11

thank you

Answer 12

Could you help me out one more time

Answer 13

sure, if i could

Answer 14

what would be the slope or m

Answer 15

cause i was trying to find the slope of the functions graph at a given point, namely (3,3)

Answer 16

slope is the derivative of the function at the given point. just put x=3 in the derivative
slope=-2(3-2)^2=-2

Answer 17

i appreciate your help

Answer 18

welcome :)