What is the equation of the line normal to # f(x)=(2x-2)^2+4x# at # x=-3#?
This is the gradient of the tangent.
So the gradient of the normal is
Equation of normal 0f #(-3,52) :
“Normal” means perpendicular to the line, or that the slopes will be opposite.
First we need to find the tangent line, which is the first derivative of the expression at x = -3.
Step-by-step solution here (long):
THEN we need to find the equation of a line perpendicular to this one (inverse slope) passing through
The final line equation is thus: