Question

Determine whether $straight g left parenthesis straight x right parenthesis space equals space cos space left parenthesis 2 straight x space plus space straight pi over 4 right parenthesis$ is increasing or decreasing for $fraction numerator 3 straight pi over denominator 8 end fraction less than straight x less than fraction numerator 7 straight pi over denominator 8 end fraction.$

Solution

Here $straight g left parenthesis straight x right parenthesis space equals space cos space open parentheses 2 straight x plus straight pi over 4 close parentheses$
$therefore space space space space straight g apostrophe left parenthesis straight x right parenthesis space equals space minus 2 space sin space open parentheses 2 straight x plus straight pi over 4 close parentheses For space space fraction numerator 3 straight pi over denominator 8 end fraction less than straight x less than fraction numerator 7 straight pi over denominator 8 end fraction comma space space space space straight g apostrophe left parenthesis straight x right parenthesis space is space positive$ .
$therefore space space space space straight g left parenthesis straight x right parenthesis space is space increasing space for space fraction numerator 3 straight pi over denominator 8 end fraction less than straight x less than fraction numerator 7 straight pi over denominator 8 end fraction.$

For Daily Free Study Material Join wiredfaculty

Application Of Derivatives

Some More Questions From Application of Derivatives Chapter

The radius of a circle is increasing uniformly at the rate of 4 cm per second Find the rate at which the area of the circle is increasing when the radius is 8 cm.

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

Phone Number

Email Address

Location