The value of $c$ in Rolle's theorem for the function $f(x) = {x^3} - 3x$ in the interval $[0,\sqrt 3 ]$ is
The value of $c$ in Rolle's theorem for the function $f(x) = {x^3} - 3x$ in the interval $[0,\sqrt 3 ]$ is
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$\Rightarrow$ $\quad 3{c^2} - 3 = 0$
$\Rightarrow$ ${c^2} = \frac{3}{3} = 1$
$\Rightarrow$ $c = \pm 1,$ where $1 \in (0,\sqrt 3 )$
therefore,$\quad c = 1$
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