Question

Find the equation of the line tangent to f(x) = 2/x-1 at the point (2, 2).

Answer 1

I found the derivative (x-1)^2

Answer 2

I got the slope 1

Answer 3

i used y-y1 = m(x-x1)

Answer 4

I got

Answer 5

(2/x) -1
or
2/(x-1)
?

Answer 6

y=1x

Answer 7

2/(x-1)

Answer 8

then your derivative is incorrect.

Answer 9

but the options I am given are. a)x+y+3=0

Answer 10

b)x-y=4 , c) y-2= (x-2)/(x-1)^2, d) y=-2x+6

Answer 11

or e) none

Answer 12

why? what did I do wrong?

Answer 13

derivative of x^n = nx^(n-1)

so, derivative of 1/x is -1/x^2

Answer 14

derivative of 2/(x-1)

= 2 derivative of (x-1)^(-1)

Answer 15

what would be next step ?

Answer 16

find the derivative? which is: - 1/(x-1)^2

Answer 17

yes,
so the derivative is -2/(x-1)^2

Answer 18

so now I insert the 2 in the x?

Answer 19

hartnn quick question. is +infin. the same as infinity?

Answer 20

yes, and yes

when we say infinity, its +infinity
when we want negative infinity, we must explicitly say -infinity

Answer 21

tell me what slope you get when you put x=2

Answer 22

-2/(2-1)^2
= -2/1
=-2

Answer 23

thank you

Answer 24

yes, you got the equation ?

Answer 25

y-y1 = m(x-x1)

Answer 26

so

Answer 27

y-2=-2(x-(-)2)
y-2 = -2(x+2)
y-2 = -2 x -4
y = -2x+6

Answer 28

you are \(\huge \color{red}{\checkmark}\)

Answer 29

thank you!!!!

Answer 30

welcome ^_^