SOLUTION: Estimate the slope of the tangent line to the graph of f(x)=x/x-2 at the point where x = 3

Algebra ->  Functions -> SOLUTION: Estimate the slope of the tangent line to the graph of f(x)=x/x-2 at the point where x = 3      Log On


   

Question 1204825: Estimate the slope of the tangent line to the graph of f(x)=x/x-2 at the point where x = 3
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
Estimate the slope of the tangent line to the graph of f%28x%29=x%2F%28x-2%29 at the point where x+=+3
first find that point
f%283%29=3%2F%283-2%29=3%2F1=3
the point where x+=+3 is (3,3)
To find the slope of the tangent line at the point (3,3), we need to take the derivative of f%28x%29+=x%2F%28x-2%29 which is y'%28x%29+=+-2%2F%28x+-+2%29%5E2

Therefore, the slope of the tangent line at the point (3,3) is

y'%283%29+=+-2%2F%283+-+2%29%5E2=-2%2F1=-2

equation of the tangent will be
y=-2x%2Bb...use point (3,3) to find b
3=-2%2A3%2Bb
b=3%2B6
b=9

and equation of the tangent is
y=-2x%2B9