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  • Explain solution RD Sharma class 12 chapter 11 Higher Order Derivatives exercise very short answer type question 8 maths

Explain solution RD Sharma class 12 chapter 11 Higher Order Derivatives exercise very short answer type question 8 maths

Answers (1)

Answer:

        \frac{d^{2} y}{d x^{2}}=\left\{\begin{array}{l} -2,0<x<1 \\ 2, x>1, x<0 \end{array}\right.

Hint:

        \text { if } y=|p| \: {\text {then }} y=\left\{\begin{array}{c} p, \text { if } 0 \leq p \leq 1 \\ -p, \text { if } p<0 \end{array}\right.

Given:

        y=\left | x-x^{2} \right |

Explanation:

It is given that

        y=\left | x-x^{2} \right |

This can be written as

        y=\left\{\begin{array}{c} x-x^{2} \text { if } 0 \leq x \leq 1 \\ -\left(x-x^{2}\right) \text { if } x<0 \text { or } x>1 \end{array}\right.

Diff y w.r to x

        \frac{d y}{d x}=\left\{\begin{array}{c} 1-2 x \text { if } 0<\mathrm{x} \leq 1 \\ -(1-2 x) \text { if } x>0 \text { or } x>1 \end{array}\right.

Di\! f\! f\; w.r.t\; to\; x

        \begin{aligned} &\frac{d^{2} y}{d x^{2}}=\left\{\begin{array}{c} -2 \text { if } 0 \leq x \leq 1 \\ -(-2) \text { if } x<0 \text { or } x>1 \end{array}\right. \end{aligned}

Thus,

        \frac{d^{2} y}{d x^{2}}=\left\{\begin{array}{l} -2,0<x<1 \\ 2, x>1, x<0 \end{array}\right.

Posted by

Gurleen Kaur

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