March 10th, 2017, 09:29 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)(x2) in (1, 2] I,ve tried https://ibb.co/bK70iv Where I've made mistake. 
March 10th, 2017, 09:44 PM  #2 
Member Joined: Sep 2016 From: India Posts: 88 Thanks: 30 
Solve quadratic equation correctly $$3x^24x1=0\\\Rightarrow \dfrac{4\pm\sqrt{16(4)(3)(1)}}{2(3)}\\\Rightarrow x=\dfrac {2\pm \sqrt 7}{3}\\\Rightarrow x=\dfrac {2+ \sqrt 7}{3}\;\text{and}\; x=\dfrac {2 \sqrt 7}{3}\\x=\dfrac {2+ \sqrt 7}{3}=1.55\in (1,\;2]\\ x=\dfrac {2 \sqrt 7}{3}=.215\notin(1,\;2]$$ Hence, $\; c=\dfrac {2+ \sqrt 7}{3}\;$ satisfies the conclusion of Rolle's theorem for the given function. 
March 11th, 2017, 04:39 AM  #3 
Math Team Joined: Jan 2015 From: Alabama Posts: 2,822 Thanks: 750 
You "dropped a sign" and used instead of the correct .


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