(C) According to the Mean Value Theorem $(MVT)$,if a function $f(x)$ is continuous on the closed interval $[a, b]$ and differentiable on the open inte

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(C) According to the Mean Value Theorem $(MVT)$,if a function $f(x)$ is continuous on the closed interval $[a, b]$ and differentiable on the open interval $(a, b)$,then there exists at least one point ${x_1}$ in the open interval $(a, b)$ such that:$f'({x_1}) = \frac{f(b) - f(a)}{b - a}$By the definition of the Mean Value Theorem,the point ${x_1}$ must lie strictly between $a$ and $b$.Therefore,$a Thus,the correct option is $C$.

Class 12 Mathematics Continuity and Differentiation Rolle’s theorem, Lagrange's mean value theorem

Medium

If from the Mean Value Theorem,$f'({x_1}) = \frac{f(b) - f(a)}{b - a}$,then

A
$a < {x_1} \le b$
B
$a \le {x_1} < b$
C
$a < {x_1} < b$
D
$a \le {x_1} \le b$

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Continuity and Differentiation

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Rolle’s theorem, Lagrange's mean value theorem

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If from the Mean Value Theorem,$f'({x_1}) = \frac{f(b) - f(a)}{b - a}$,then

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