# What is the equation of the line normal to #f(x)=(5-x)^2 # at #x=2#?

##### 1 Answer

Feb 15, 2016

#### Explanation:

Given

Its general slope is given by the derivative:

At

and a line normal to it (i.e. perpendicular to it) will have a slope

At

giving a point

Using the slope-point form for the normal line

We can simplify this as

or (in standard form)

graph{(y-(5-x)^2)(x-6y+52)=0 [-7.83, 14.67, -0.585, 10.665]}