Question

The value of $c$ in Rolle's theorem for the function $f(x) = x^3 - 3x$ in the interval $\left[0, \sqrt{3}\right]$ is

• A. $1$
• B. $-1$
• C. $\frac{3}{2}$
• D. $\frac{1}{3}$

Answer 1

Answer: (A)

$1$

Answer 2

Since Rolle's theorem satisfy in $\left[0, \sqrt{3}\right]$. $\therefore f '\left(c\right)=0$ $\Rightarrow 3c^{2}-3=0$ $\Rightarrow c^{2}-1$ $\Rightarrow c \pm1$ $\Rightarrow c=1 \left(\because c=-1 \notin\left[0, \sqrt{3}\right]\right)$