Question

find an equation of the tangent line to the graph of the function at the indicated point..... F(x)=x/(x-1) point--(2,2)
I know the answer is y=-x+4 but don't know how to get to it please help!!

Answer 1

is this a calculus question?

Answer 2

yeah sort of i know a little calculus....

Answer 3

i know that fprime(x)= -1/(x-2)^2

Answer 4

but dont know what to do from there..

Answer 5

whoops i mean fprime(x)= -1/(x-1)^2

Answer 6

the slope of the tangent line is the derivative so get the derivative of x/(x-1) \[\frac{x - (x-1)}{(x-1)^2} = \frac{x - x + 1}{(x-1)^2} = \frac{1}{(x-1)^2}\]

Answer 7

do you get that?

Answer 8

oops...

Answer 9

but isn't it fprime(x)*g(x)-gprime(x)*f(x)/g(x)^2

Answer 10

\[\frac{x-1 - x}{(x-1)^2}\] lol sorry

Answer 11

yeah okay so what do i do after that?

Answer 12

since \(-\frac{1}{(x-1)^2}\) is the slope we use the formula \[y - y_1 = m (x - x_1)\]

Answer 13

we plug in (2, 2)

\[y - 2 = -\frac{1}{(2 - 1)^2} (x - 2)\] \[y - 2 = -1(x - 2)\]

Answer 14

\[y - 2 = -x + 2\] \[y = -x + 2 + 2\] \[y = -x + 4\]

Answer 15

thanks! :)

Answer 16

yw