My Math Forum Rolle's Theorem.

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 March 10th, 2017, 08:29 PM #1 Newbie   Joined: Mar 2017 From: US Posts: 1 Thanks: 0 Rolle's Theorem. Find the number 'c' that satisfies the conclusion of Rolle's theorem for the function f(x) = (x² -1)(x-2) in (1, 2] I,ve tried https://ibb.co/bK70iv Where I've made mistake.
 March 10th, 2017, 08:44 PM #2 Member   Joined: Sep 2016 From: India Posts: 88 Thanks: 30 Solve quadratic equation correctly $$3x^2-4x-1=0\\\Rightarrow \dfrac{4\pm\sqrt{16-(4)(3)(-1)}}{2(3)}\\\Rightarrow x=\dfrac {2\pm \sqrt 7}{3}\\\Rightarrow x=\dfrac {2+ \sqrt 7}{3}\;\text{and}\; x=\dfrac {2- \sqrt 7}{3}\\x=\dfrac {2+ \sqrt 7}{3}=1.55\in (1,\;2]\\ x=\dfrac {2- \sqrt 7}{3}=-.215\notin(1,\;2]$$ Hence, $\; c=\dfrac {2+ \sqrt 7}{3}\;$ satisfies the conclusion of Rolle's theorem for the given function.
 March 11th, 2017, 03:39 AM #3 Math Team   Joined: Jan 2015 From: Alabama Posts: 2,649 Thanks: 680 You "dropped a sign" and used $\sqrt{16- 12}$ instead of the correct $\sqrt{16+ 12}$.

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