The normal line is the line that is perpendicular to the tangent line.

First we will find the tangent line at the point (0,0).

f(x)= 2xe^x

==> The slope of the tangent line is the derivative at x= 0

==> f'(x)= (2x)'e^x + 2x(e^x)'

==> f'(x)= 2e^x + 2xe^x

==> f'(0) = 2e^0 + 2(0)e^0

==> f'(0) = 2

Then the slope of the tangent line is m= 2

==> y-y1 = m(x-x1)

==> y= 2x

**Then, the tangent line is** : `y= 2x`

`` Now we will find the slope of the normal line.

Since the normal line is perpendicular to the tangent line, then the slope is -1/2

==> y= (-1/2)x

**Then, the normal line is** :`y= -1/2 x`

## We’ll help your grades soar

Start your 48-hour free trial and unlock all the summaries, Q&A, and analyses you need to get better grades now.

- 30,000+ book summaries
- 20% study tools discount
- Ad-free content
- PDF downloads
- 300,000+ answers
- 5-star customer support

Already a member? Log in here.

Are you a teacher? Sign up now