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Question

The greatest value of sin3x+cos3x in [0,π2] is

A
1
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B
2
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C
3
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D
4
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Solution

The correct option is C 1
f(x)=sin3x+cos3x
f(x)=3sinxcosx(sinxcosx)
For maxima or minma,
f(x)=0
sinx=0;cosx=0;sinxcosx=0
x=0,π2,π4
f′′(π4)>0
So, f(x) has a minimum at x=π4
f(0)=1 and f(π2)=1
So, the maximum value of f(x) is 1.

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