SOLUTION: Find the equation of the tangent line to the graph of f(x)= 5-2 lnx at x=1

Algebra ->  Test -> SOLUTION: Find the equation of the tangent line to the graph of f(x)= 5-2 lnx at x=1      Log On


   

Question 1135494: Find the equation of the tangent line to the graph of f(x)= 5-2 lnx at x=1
Answer by ikleyn(52798) About Me  (Show Source):
You can put this solution on YOUR website!
.
First find the slope m, which is exactly the derivative of the function at x= 1:


    m = %28df%29%2F%28dx%29 = -2%2A%281%2Fx%29 = -2  at  x= 1.


You also need to know the value of the given function at x= 1. It is


    f(1) = 5 - 2*ln(1) = 5 - 2*0 = 5.


Thus the equation of the tangent line is


    y -5 = (-2)*(x-1),   or

    y - 5 = -2x + 2.


Now you can transform it to any form you want.  For example,  


    2x + y = 7.

Answered and solved.