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  • Need solution for RD Sharma maths class 12 chapter 10 Differentiation exercise Fill in the blanks question 3

Need solution for RD Sharma maths class 12 chapter 10 Differentiation exercise Fill in the blanks question  3

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Answer:  f^{1}(2)=3

Hint: f(x)=\left(\begin{array}{ll} x-x^{2} & x^{2}-x \leq 0 \\ x^{2}-x & x^{2}-x \geq 0 \end{array}\right)

Given: f(x)=\left|x^{2}-x\right|

Solution:  f(x)=\left|x^{2}-x\right|

f(x)=\left(\begin{array}{cc} -\left(x^{2}-x\right) & x^{2}-x<0 \\ x^{2}-x & x^{2}-x \geq 0 \end{array}\right)

\begin{aligned} &f(x)=\left(\begin{array}{cc} \left(x-x^{2}\right) & x^{2}-x<0 \\ x^{2}-x & x^{2}-x \geq 0 \end{array}\right) \\\\ &f^{{}'}(x)=\left(\begin{array}{cc} (1-2 x) & x^{2}-x<0 \\ 2 x-1 & x^{2}-x \geq 0 \end{array}\right) \end{aligned}

\begin{aligned} &f^{{}'}(2)=2 x-1 \\\\ &=2(2)-1 \\\\ &=3 \end{aligned}

 

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