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Question

Find intervals in which the function given by f(x)=sin3x,x[0,π2] is decreasing.

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Solution

f(x)=sin3x
f(x)=3cos3x
f(x)=0
cos3x=0
x=π6,π2
Take (0,π6)+(π6,π2)
x(0,π6)+x(π6,π2)
03x<π2
cos3x<0
cos3x>0 when 03x<π2
f(x)<0
f(x)>0
f(x) is increasing in (0,π6)
f(x) is decreasing in (π6,π2)

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