Value of ‘c’ of Lagrange’s mean theorem for f(x)=2+x3, if x 1 on [−1,2]is

f1(c)=f(b)−f(a)b−a⇒3c2=6−12+1⇒c=±53

Value of ‘c’ of Lagrange’s mean theorem for f(x)=2+x3, if x 1 on [−1,2]is

f1(c)=f(b)−f(a)b−a⇒3c2=6−12+1⇒c=±53

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Value of ‘ $c$ ’ of Lagrange’s mean theorem for $f (x) = \{\begin{array}{ll} 2 + x^{3}, if x < 1 \\ 3 x, if x > 1 \end{array} on [- 1, 2]$ is

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$\pm \frac{3}{\sqrt{5}}$

$\pm \frac{\sqrt{5}}{3}$

$\pm \frac{\sqrt{3}}{2}$

$\pm \frac{\sqrt{2}}{5}$

answer is A.

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Detailed Solution

$f^{1} (c) = \frac{f (b) - f (a)}{b - a} \Rightarrow 3 c^{2} = \frac{6 - 1}{2 + 1} \Rightarrow c = \pm \frac{\sqrt{5}}{3}$

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