Q113
Let the function \[ f ( ) = | array*20c & & \\ ( /6 )& ( /6 )& ( /6 ) \\ ( /3 )& ( /3 )& ( /3 ) array |\] where \[ [ /6,\, /3 ]\] and \[ f' ( )\] denote the derivative of f with respect to \[ \]. Which of the following statements is/are TRUE? I. There exists \[ ( /6,\, /3 )\] such that \[ f' ( ) = 0.\] II. There exists \[ ( /6,\, /3 )\] such that \[ f' ( ) 0\]
Let the function
{\text{f}}\left( \theta \right) = \left| {\begin{array}{*{20}{c}} {\sin \theta }&{\cos \theta }&{\tan \theta } \\ {\sin \left( {\frac{\pi }{6}} \right)}&{\cos \left( {\frac{\pi }{6}} \right)}&{\tan \left( {\frac{\pi }{6}} \right)} \\ {\sin \left( {\frac{\pi }{3}} \right)}&{\cos \left( {\frac{\pi }{3}} \right)}&{\tan \left( {\frac{\pi }{3}} \right)} \end{array}} \right|
where and denote the derivative of f with respect to . Which of the following statements is/are TRUE?
I. There exists such that
II. There exists such that
{\text{f}}\left( \theta \right) = \left| {\begin{array}{*{20}{c}} {\sin \theta }&{\cos \theta }&{\tan \theta } \\ {\sin \left( {\frac{\pi }{6}} \right)}&{\cos \left( {\frac{\pi }{6}} \right)}&{\tan \left( {\frac{\pi }{6}} \right)} \\ {\sin \left( {\frac{\pi }{3}} \right)}&{\cos \left( {\frac{\pi }{3}} \right)}&{\tan \left( {\frac{\pi }{3}} \right)} \end{array}} \right|
where and denote the derivative of f with respect to . Which of the following statements is/are TRUE?
I. There exists such that
II. There exists such that
A.
l only
B.
ll only
C.
Both l and ll
AnswerD.
Neither l nor ll
Answer: Option C
Solution
Answer: Option C
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