What is the equation of the normal line of #f(x)=12x^3-4x^2-5x# at #x=-2#?
Normal line will be perpendicular to the tangent line. As we know that the product of perpendicular gradients is always
We compute the slope of the tangent by evaluating the first derivative:
So the slope of the normal (
To calculate the equation of the normal line we use
To use this, we need a point on the line. We know that x = -2 is on the line, so we evaluate the original function at this point to get :