# What is the equation of the line normal to # f(x)=(x+5)(x+2)+2x^2-8x+2# at # x=0#?

##### 1 Answer

It is

#### Explanation:

The strategy is to find first the slope of the tangent line than we can easily find the orthogonal.

The slope of the tangent is given by the derivative evaluate in

Before doing the derivative I do the product between the parenthesis and reorder the terms

Now for the derivative

then when

This is the the slope of the tangent line passing from

The slope of the normal line is the opposite inverse of this:

We need now to find the intercept and to do this we impose the passage for the point

The equation is

Then the final equation of the normal line is