Question

Separate $open square brackets 0 comma space space space straight pi over 2 close square brackets$ into sub-intervals in which the function f (x) = sin 3x is increasing or decreasing.

Solution

Here $straight f left parenthesis straight x right parenthesis space equals space sin space 3 straight x space space space space space space space rightwards double arrow space space space space space straight f apostrophe left parenthesis straight x right parenthesis space equals space 3 space cos space 3 straight x$
(i) For f(x) to be increasing, f '(x) > 0
$therefore space space space space 3 space cos space 3 straight x space greater than 0 space space space space space space space space space space rightwards double arrow space space space space cos space 3 straight x space greater than 0 space space space space space space space space rightwards double arrow space space space space straight x space element of space open parentheses 0 comma space space straight pi over 6 close parentheses therefore space space space space straight f left parenthesis straight x right parenthesis space increases space in space open parentheses 0 comma space straight pi over 6 close parentheses$
(ii) For f(x) to be decreasing, f '(x) < 0
$therefore space space space space 3 space cos space 3 straight x space less than 0 space space space space space rightwards double arrow space space space space cos space 3 straight x space less than space 0 space space space space space space space space rightwards double arrow space straight x space element of space space space open parentheses straight pi over 6 comma space space straight pi over 2 close parentheses therefore space space space space straight f left parenthesis straight x right parenthesis space decreases space in space open parentheses straight pi over 6 comma space space straight pi over 2 close parentheses.$

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Application Of Derivatives

Separate $open square brackets 0 comma space space space straight pi over 2 close square brackets$ into sub-intervals in which the function f (x) = sin 3x is increasing or decreasing.

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For Daily Free Study Material Join wiredfaculty

Application Of Derivatives

Separate into sub-intervals in which the function f (x) = sin 3x is increasing or decreasing.

Some More Questions From Application of Derivatives Chapter

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

Separate $open square brackets 0 comma space space space straight pi over 2 close square brackets$ into sub-intervals in which the function f (x) = sin 3x is increasing or decreasing.