SOLUTION: Find the equation of the line with slope -1 that is the tangent to the curve y=1/x-1.

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Question 254181: Find the equation of the line with slope -1 that is the tangent to the curve y=1/x-1.
Answer by drk(1908) About Me  (Show Source):
You can put this solution on YOUR website!
The question was: slope -1 that is the tangent to the curve y=1/x-1
step 1 - take the derivative of y to get
(i) y' = %28%28x-1%29%2A0+-+1%2A%281%29%29+%2F+%28x-1%29%5E2
which simplifies to
(ii) y' = %28+-+1%29+%2F+%28x-1%29%5E2.
Now slope = -1 means derivative = -1. We get from (ii)
(iii) -1+=+-1%2F%28x-1%29%5E2
Solving we get
(x-1)^2 = 1
(x-1) = +-1
X = 0 or x = 2
We have two coordinates: (0,1) and (2,1)
So, we have y = mx + b with (0,1) to get
1 = 0*-1 + b
b = 1
The first equation is
Y = -1x + 1.
Now, we have y = mx + b with (2,1) to get
1 = 0*2 + b
b = 1
The second equation is
Y = -1x + 1.
So, it appears that we have
Y = -1x + 1