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)(x2) 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 $$3x^24x1=0\\\Rightarrow \dfrac{4\pm\sqrt{16(4)(3)(1)}}{2(3)}\\\Rightarrow x=\dfrac {2\pm \sqrt 7}{3}\\\Rightarrow x=\dfrac {2+ \sqrt 7}{3}\;\text{and}\; x=\dfrac {2 \sqrt 7}{3}\\x=\dfrac {2+ \sqrt 7}{3}=1.55\in (1,\;2]\\ x=\dfrac {2 \sqrt 7}{3}=.215\notin(1,\;2]$$ Hence, $\; c=\dfrac {2+ \sqrt 7}{3}\;$ satisfies the conclusion of Rolle's theorem for the given function. 
March 11th, 2017, 03:39 AM  #3 
Math Team Joined: Jan 2015 From: Alabama Posts: 3,264 Thanks: 902 
You "dropped a sign" and used instead of the correct .


Tags 
rolle, theorem 
Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
Rolle's Theorem Help  Azilips  Calculus  4  March 17th, 2016 11:46 AM 
Help with Rolle's Theorem [2]  Shamieh  Calculus  4  October 21st, 2013 04:18 PM 
Applying Rolle's Theorem  bobcantor1983  Calculus  1  October 1st, 2013 01:49 PM 
Rolle's Theorem 2  mathkid  Calculus  4  October 6th, 2012 06:35 PM 
Rolle's Theorem  mathkid  Calculus  2  October 6th, 2012 07:17 AM 