Find all the critical numbers of the function fxsin26x cos6

Find all the critical numbers of the function f(x)=sin^2(6x) + cos6x
0<x<pi/3. give exact answer

f \'(x) = 12sin(6x)cos(6x) - 6sin(6x) ...... = 6sin(6x)(2cos(6x) - 1) f(x) has a critical number where f \'(x) = 0, so set each factor to zero. sin(6x) = 0 OR 2cos(6x) - 1 = 0 The first equation is true if 6x = pi i.e., x = pi/6 The second equation is true if: 6x = pi/3 OR if: 6x = 5pi/3 , which gives two more solutions, namely x = pi/18 OR x = 5pi/18 Critical numbers are: pi/18 , pi/6 , 5pi/18

$Find all the critical numbers of the function f(x)=sin^2(6x) + cos6x 0<x<pi/3. give exact answerSolution f \'(x) = 12sin(6x)cos(6x) - 6sin(6x) ...... = 6s$

Find all the critical numbers of the function fxsin26x cos6

Solution

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