Calculus with Applications (10th Edition)

Let $f(x)=a x^{3}+b x^{2}+c x+d$ is cubic function where $a, b, c$ and $d$ are constant and $a \neq 0$ Since \begin{align*} f'(x)&=\frac{d}{dx}(a x^{3}+b x^{2}+c x+d)\\ &=3ax^2+2bx+c,\ \ \ a\neq 0 \end{align*} Then $f^{\prime}(x)$ is a quadratic function. Hence derivative function of any third degree function will be a second degree function. i.e a quadratic function.