SOLUTION: Write an equation of a tangent to the curve at a given point: y=2x-1/x at P(0.5,-1)

Algebra ->  Vectors -> SOLUTION: Write an equation of a tangent to the curve at a given point: y=2x-1/x at P(0.5,-1)      Log On


   

Question 182408: Write an equation of a tangent to the curve at a given point:
y=2x-1/x at P(0.5,-1)
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
The slope of the tangent line is the value of the derivative of the function at that point.
First, find the derivative of the function.
y=2x-1%2Fx=2x-x%5E%28-1%29
dy%2Fdx=2-%28-1%29x%5E%28-2%29=2%2B1%2Fx%5E2
At x=0.5,
%28dy%2Fdx%29=2%2B1%2F%280.5%29%5E2=6
Now you have the slope of the line, use the point-slope form of the line,
y-y%5Bp%5D=m%28x-x%5Bp%5D%29
y-%28-1%29=6%28x-0.5%29
y%2B1=6x-3
y=6x-4
.
.
.