find the equation of the tangent line

Question

Find the equation of the tangent line to the curve at the given point.\\ y=1+2x-x³, (1,2)

y=

Answer 1

This is a standard type of problem.

 

The first step is to find the derivative of the function 1 + 2 x - x³    at the point (1,2)

 

y'  =   2 - 3 x²      which evaluates to   -1   for x = 1.       Thus the slope of the

desired tangent line is -1.         The next step is to use the algebra 1 formula for a line when

the slope and one point on it are given:

    (y- y1 ) =   m  (x -x1)     for the case here

     y-2  =  - (x-1)      which  can be written as 

   y = -x +3