# What is the equation of the line normal to #f(x)=x^2-x # at #x=-2#?

##### 1 Answer

#### Explanation:

The normal line will intersect the curve at

To find the slope of the normal line, first find the slope of the tangent line at that point by finding the value of the derivative at

Through the power rule, we see that

The slope of the normal line is then

Using the point

#6=1/5(-2)+b" "=>" "b=32/5#

The normal line is:

#y=1/5x+32/5#

Graphed are

graph{(y-x^2+x)(-y+1/5x+32/5)=0 [-15.61, 12.86, -1.46, 12.77]}