Work Step by Step
A cubic function is any function where the highest degree is three, so it can be written as any function $f(x)=ax^3+bx^2+cx+d$, where $a\ne0$. The derivative of $f(x)$ is $f'(x)=3ax^2+2bx+c$. A quadratic polynomial is a polynomial whose highest degree is two. Since $a$ cannot equal zero, the highest degree must be two and the derivative must be a quadratic polynomial.