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