Determine the derivative of the function ƒ(x) = x^3 − 12x^2. Now determine the derivative of the function g(x) = x^3 − 12x^2 + 6. How are the two functions related? How are the derivatives of the two functions related?

Answer 1

These are the family of parabolas with same slope only difference is in the constant which has been added in g(x)
f'(x)=g'(x)=3x^2 - 24x.