What is the extreme cos(x)+sin(x) ?

The extreme cos(x)+sin(x) is Maximum(pi/4+2pin,sqrt(2)),Minimum((5pi)/4+2pin,-sqrt(2))

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extreme cos(x)+sin(x)

extreme points

cos (x) + sin (x)

Maximum (\frac{π}{4} + 2 πn, 2), Minimum (\frac{5 π}{4} + 2 πn, - 2)

Solution steps

Find the critical points:

x = \frac{π}{4} + 2 πn, x = \frac{5 π}{4} + 2 πn

Domain of

cos (x) + sin (x) : - \infty < x < \infty

Find intervals:

Increasing

: 2 πn \leq x < \frac{π}{4} + 2 πn,

Decreasing

: \frac{π}{4} + 2 πn < x < \frac{5 π}{4} + 2 πn,

Increasing

: \frac{5 π}{4} + 2 πn < x < 2 π + 2 πn

Plug the extreme point

x = \frac{π}{4} + 2 πn

into

cos (x) + sin (x) \Rightarrow y = 2

Maximum (\frac{π}{4} + 2 πn, 2)

Plug the extreme point

x = \frac{5 π}{4} + 2 πn

into

cos (x) + sin (x) \Rightarrow y = - 2

Minimum (\frac{5 π}{4} + 2 πn, - 2)

Maximum (\frac{π}{4} + 2 πn, 2), Minimum (\frac{5 π}{4} + 2 πn, - 2)

(x + 3) (- x^{2} + 16)

f (x) = 1.0106 x

f (x) = \frac{- 5}{x + 6}

f (x) = \frac{x - 3}{x - 10}

What is the extreme cos(x)+sin(x) ?
The extreme cos(x)+sin(x) is Maximum(pi/4+2pin,sqrt(2)),Minimum((5pi)/4+2pin,-sqrt(2))