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  • Explain solution for RD Sharma class 12 chapter Mean value theorem exercise 14.1 question 1 sub question 6 math

Explain solution for RD Sharma class 12 chapter Mean value theorem exercise 14.1 question 1 sub question 6 math

Answers (1)

Answer:

Rolle’s Theorem is not applicable on f(x) in [0,

             

Given:

               f (x) = \left\{\begin{matrix} -4x +5 , 0 \leq x \leq 1\\ 2x-3,1\leq x \leq 2 \end{matrix}\right.

Explanation:

We have

               f (x) = \left\{\begin{matrix} -4x +5 , 0 \leq x \leq 1\\ 2x-3,1\leq x \leq 2 \end{matrix}\right.

For  n = 1

           \qquad \begin{aligned} \text { L.H.S } &=\lim _{x \rightarrow(1-h)}[-4 x+5] \\\\ &=\lim _{h \rightarrow 0}[-4(1-h)+5] \\\\ &=-4+5=1 \\\\ \text { R.H.S } &=\lim _{x \rightarrow(1+h)}[2 x-3] \\\\ &=\lim _{h \rightarrow 0}[2(1+h)-3] \\\\ &=2-3=-1 \end{aligned} \\

                           L.H.S \neq R.H.S

f (x) is not continuous at   x = 1 \in [0,2]

Rolle’s Theorem is not applicable on f (x) in [0,2] 

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