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CONTINUITY AND DIFFERENTIABILITY — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsCONTINUITY AND DIFFERENTIABILITY2 Marks
Question
Find the value of c in Rolle’s theorem for the function $\text{f(x)} = \text{x}^{3} - \text{3x in} [ -\sqrt{3}, 0].$
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Answer

$\text{f(x)} = \text{x}^{3} - \text{3x}$
$\therefore \text{f}'\text{(c)} = 3\text{ c}^{2} - 3 = 0$
$\therefore \text{c}^{2} = 1 \Rightarrow \text{c} = \pm 1.$
Rejecting c = 1 as it does not belong to $(-\sqrt{3, 0)},$
we get c = –1.

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