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#### Please solve RD Sharma class 12 chapter Mean value theorem exercise 14.1 question 1 sub question 4 maths textbook solution

Rolle’s Theorem is not applicable  [1,3]

Hint:

$f (x)$ is continuous for all x and hence continuous in [1,3]

Given:

$f (x) = 2x^2 - 5x +3$ on [1,3]

Explanation:

We have

$f (x) = 2x^2 - 5x +3$

1.Being polynomial$f (x)$ is continuous for all x and hence continuous in [1,3]

2. $f (x') = 4x -5$, which exists in (1,3)

$\therefore f (x)$ is derivable in (1,3)

3.

\begin{array}{l} \\ f(1)=2(1)^{2}-5(1)+3\\ \begin{aligned} &=2-5+3=-3+3=0 \\ f(3)=& 2(3)^{2}-5(3)+3 \\ &=2 \times 9-15+3 \\ &=18-15+3=3+3=6 \\ \therefore f(1) & \neq f(3) \end{aligned} \end{array}

Thus third condition of Rolle’s Theorem is not satisfied.

Hence, Rolle’s Theorem is not applicable.