+91-8076753736 [email protected]

-->

Application Of Derivatives

Question

Wired Faculty App

Find the maximum and minimum value of x + sin 2 x on $left square bracket 0 comma space 2 straight pi right square bracket$ .

Solution

Let space straight f left parenthesis straight x right parenthesis space equals space straight x plus sin space 2 straight x

therefore space space space straight f apostrophe left parenthesis straight x right parenthesis space space equals space 1 plus 2 space cos space 2 straight x space space space space space space space space space space space space space space straight f apostrophe left parenthesis straight x right parenthesis space equals space 0 space space space space space space rightwards double arrow space space space space space 1 plus 2 space cos 2 straight x space equals space 0 rightwards double arrow space space space space cos space 2 straight x space equals space minus 1 half space equals space minus cos space 60 degree space equals space minus cos space straight pi over 3 rightwards double arrow space space space cos space 2 straight x space space equals cos space open parentheses straight pi minus straight pi over 3 close parentheses comma space space space cos space open parentheses straight pi plus straight pi over 3 close parentheses comma space space space cos space open parentheses 3 straight pi minus straight pi over 3 close parentheses space cos space open parentheses 3 straight pi plus straight pi over 3 close parentheses rightwards double arrow space space space space space 2 straight x space equals space fraction numerator 2 straight pi over denominator 3 end fraction comma space space fraction numerator 4 straight pi over denominator 3 end fraction comma space fraction numerator 8 straight pi over denominator 3 end fraction comma space space fraction numerator 10 straight pi over denominator 3 end fraction rightwards double arrow space space space space space space space space space space space straight x space equals space straight pi over 3 comma space space fraction numerator 2 straight pi over denominator 3 end fraction comma space fraction numerator 4 straight pi over denominator 3 end fraction comma space space fraction numerator 5 straight pi over denominator 3 end fraction

straight f left parenthesis 0 right parenthesis space equals space 0 plus sin space 0 space equals space 0 plus 0 space equals space 0 straight f open parentheses straight pi over 3 close parentheses space equals space straight pi over 3 plus sin space fraction numerator 2 straight pi over denominator 3 end fraction space equals space straight pi over 3 plus fraction numerator square root of 3 over denominator 2 end fraction straight f open parentheses fraction numerator 2 straight pi over denominator 3 end fraction close parentheses space equals space fraction numerator 2 straight pi over denominator 3 end fraction plus sin space fraction numerator 4 straight pi over denominator 3 end fraction space equals space fraction numerator 2 straight pi over denominator 3 end fraction minus fraction numerator square root of 3 over denominator 2 end fraction straight f open parentheses fraction numerator 4 straight pi over denominator 3 end fraction close parentheses space equals space fraction numerator 4 straight pi over denominator 3 end fraction plus sin space fraction numerator 8 straight pi over denominator 3 end fraction space equals space fraction numerator 4 straight pi over denominator 3 end fraction plus fraction numerator square root of 3 over denominator 2 end fraction straight f open parentheses fraction numerator 5 straight pi over denominator 3 end fraction close parentheses space equals space fraction numerator 5 straight pi over denominator 3 end fraction plus sin space fraction numerator 10 straight pi over denominator 3 end fraction space equals space fraction numerator 5 straight pi over denominator 3 end fraction minus fraction numerator square root of 3 over denominator 2 end fraction

straight f left parenthesis 2 straight pi right parenthesis space equals space 2 space straight pi space plus space sin space 4 straight pi space equals space 2 straight pi plus 0 space equals space 2 straight pi

therefore space space space max space. value space space equals space 2 straight pi comma space space min. space value space equals space 0

Some More Questions From Application of Derivatives Chapter

Mock Test Series

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation