What is the equation of the line normal to # f(x)=(x-4)(x-2)+2x^2-3x+4# at # x=0#?
Let's simplify the function first.
As next, to find the slope of the tangent and normal line, we need to compute the derivative of the function:
Evaluating the derivative at
The slope of the normal line at
Now, we have the slope of the normal line and we have the
The normal line can be described via the line equation
Plug the values
So, the equation of the normal line is