Find the value of $c$ which satisfies Rolle's Theorem for the function $f(x)=x^3-12x$ on the interval $[0,2\sqrt3]$.
So I know that I have to take the derivative in problem 1, but after that I am clueless.
2026-02-23 21:48:35.1771883315
Find the value of $c$ which satisfies Rolle's Theorem for the function $f(x)=x^3-12x$ on the interval $[0,2\sqrt3]$.
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The function $f(x) = x^3 - 12x$ satisfies the conditions for Rolle's theorem in $[0,2\sqrt{3}]$. That means that : $\exists x_0 \in [0,2\sqrt{3}] : f'(x_0) =0 \Leftrightarrow 3x^2 - 12 = 0 \Leftrightarrow x_0^2 = 4 \Leftrightarrow x_0=2 $ or $x_0=-2$. But you want $ x_0 \in [0,2\sqrt{3}]$ so that $x_0 = 2$.