# What is the equation of the normal line of f(x)= e^(x^2+x-12) at x = 3?

Dec 20, 2015

I found:
$y = - \frac{1}{7} x + \frac{10}{7}$

#### Explanation:

Here I would first find the slope $m$ of the TANGENT of your function at $x = 3$.
Then I would evaluate the slope $m '$ of the PERPENDICULAR as:
$m ' = - \frac{1}{m}$
Finally I would use the relationship:
$y - {y}_{0} = m ' \left(x - {x}_{0}\right)$ to find the required equation.
So: