The maximum value of sinx +cosx, 0

Hello student,

Consider the interval [0,2pi]
Let f(x)= sinx+cosx
f'(x)=cosx-sinx
For maxima and minima
f'(x)=0
=> cosx-sinx=0=>tanx=1
=> x = pi/4,5pi/4
f(x) at x =0, pi/4 , 5pi/4 , 2pi
f(0)=1
f(pi/4)=root2
f(5pi/4)=-root2
f(2pi)=1
Hence the maximum value of f(x)= sqrt(2)

Thanks and Regards

Shaik Aasif

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