SOLUTION: Please help me solve this problem: Find the equation of the line with slope -1
that is the tangent to the curve y = 1/x-1.
(1 mark ea
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-> SOLUTION: Please help me solve this problem: Find the equation of the line with slope -1
that is the tangent to the curve y = 1/x-1.
(1 mark ea
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Question 257523: Please help me solve this problem: Find the equation of the line with slope -1
that is the tangent to the curve y = 1/x-1.
(1 mark each for the general equation of the line, for getting the quadratic, for solving for k and for the solution)(Advanced functions)
I have started with the slope of -1 is in the form of y= -x+k (k is used instead of b to prevent confusion with the quadratic). The intersection of
this line with the curve y= 1/x-1 is found by solving -x+k = 1/x-1.
Rearranging the equation :
Then I would like to use the discriminant formula to solve for k, however, I am not sure how, and, if I have rearranged the equation correctly. I would appreciate your help with solving this problem. Thank you. Answer by MRperkins(300) (Show Source):
You can put this solution on YOUR website! -x+k = 1/x-1.
-x+k+1=1/x
-x^2+kx+x=1
-x^2+kx+x-1=0
-x^2+(k+1)x-1=0
a=-1
b=(k+1)
c=-1
(k+1)^2-4(-1)(-1)=0
(k+1)^2-4=0
(k+1)^2=4
k+1=2
k=1
So y=-x+1 would be the equation of the tangent line.
I used a graphing calculator to verify that these equations at least look right and they do.
