Equation of the Tangent Line...1

Find the equation of the tangent line to the parabola y = x^2 at the point P (1, 1).

1. What is a tangent line?

2. How is this done?

 

1. What is a tangent line?
a line that touches parabola at given point

2.
the tangent line to the parabola y = x^2 at the point P (1, 1)
first find a slope of the tangent line y=mx+b
derivate y = x^2
(d/dx)(x^2)=2x
(d/dx)(x)=2x
(d/dx)(x)=2x....find (d/dx)(1)
(d/dx)(x)=2 -> a slope is m=2

tangent line, so far, is y=2x+b
use given point to calculate b

1=2*1+b
b=1-2
b=-1

and, equation of the tangent line is: y=2x-1

 

Is there a way to do this without finding the derivative? I want to travel one chapter and section at a time.

 

you have to use derivative

 

Ok. Will do.