The local maxima of the funtion f(x)=sinx+cosx∀x∈[0,π2] is
A
1
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B
√2
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C
12
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D
13
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Solution
The correct option is B√2 f(x)=sinx+cosx⇒f′(x)=cosx−sinx=0⇒x=π4 f′′(x)=−sinx−cosx<0atx=π4 So the function will be maximum and the maximum value is, f(π4)=√2