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March 10th, 2017, 09:29 PM   #1
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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.
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March 10th, 2017, 09:44 PM   #2
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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.
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March 11th, 2017, 04:39 AM   #3
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You "dropped a sign" and used instead of the correct .
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