Question

If y = |x − x²|, then find \[\frac{d^2 y}{d x^2}\] ?

Answer 1

Here,

\[y = \left| x - x^2 \right|\]
\[ = \binom{x - x^2 \text { if }0 < x < 1}{ - x + x^2\text { if } x > 1, x < 0}\]
\[ \Rightarrow \frac{d y}{d x} = \binom{1 - 2x \text { if }0 < x < 1}{ - 1 + 2x\text {  if }x > 1, x < 0}\]
\[ \Rightarrow \frac{d^2 y}{d x^2} = \binom{ - 2 \text{ if }0 < x < 1}{2 \text { if } x > 1, x < 0}\]