What is the maximum value of the function `s in" "x" "+" "cos" "x` ?

Explanation

`f(x) = sin x + cos x `
` rArr f'(x) = cos x - sin x`
For maxima/minima
`f'(x) = 0 rArr cos x - sin x = 0`
`rArr cos x = sin x rArr x = pi/4`
Now` f''(x) =- sin x - cos x`
at ` x = pi//4`,
`f''(pi/4) =- sin.(pi/4) - cos. pi/4`
` =- 1/sqrt2 - 1/sqrt2 =- sqrt2 lt 0`
`:. f(x)" is maximum at "x=pi/4`.
Maximum value = `f(pi/4) = sin.pi/4 + cos.pi/4`
` = 1/sqrt2+1/sqrt2= sqrt2`