Question

Find an equation for each tangent to the curve y=1/(x-1) that has slope -1.

Answer 1

take the derivative, set it equal to \(-1\) and solve for \(x\)

Answer 2

ohhh okay, thanks i'll try that!

Answer 3

oh yeah. haha. misunderstood it i gues.

Answer 4

okay so i tried doing that and the answer i got was wrong.

Answer 5

this is how i tried doing it...

Answer 6

cancel out the minus sign from both sides

Answer 7

where?

Answer 8

-1/(x-1)(x-1) = -1
hence

(x-1)(x-1) = 1

you gt x =0,2

Answer 9

okay i see that, thanks him1618. but now how do i find the equations of the tangents?

Answer 10

See..you need a slope and a point dont yu?

Answer 11

\[-\frac{1}{(x-1)^2}=-1\]
\[\frac{1}{(x-1)^2}=1\]
\[(x-1)^2=1\]
\[x-1=1\]or \(x-1=-1\) so \(x=0\) or \(x=2\)

Answer 12

for any line you need a slope and a point....see if you already have them

Answer 13

?

Answer 14

um (0, -1) and (2, 1)

Answer 15

yes...do you have the corresponding slopes?

Answer 16

um wouldn't it just be -1 for both?

Answer 17

true..now find both the lines

Answer 18

am i using the y-y1=m(x-x1) formula?

Answer 19

yes

Answer 20

thank you so much! i got the right answers :)
@ x=0 y=-x-1
@ x=2 y=-x+3