If y = |x – x^2|, then find d^2y/dx^2.

Question

If y = |x – x²|, then find \(\frac{d^2y}{dx^2}.\)

Answer 1

Given:

y = |x - x²|

y = \(\begin{cases}x-x^2;&x\geq0\\x^2-x;&x\leq0\end{cases}\)

\(\frac{dy}{dx}=\begin{cases}1-2x;&x\geq0\\2x-1;&x\leq0\end{cases}\)

\(\frac{d^2y}{dx^2}=\begin{cases}-2;&x\geq0\\2;&x\leq0\end{cases}\)