What is the extreme 2cos(x)+2sin(x) ?

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

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extreme 2cos(x)+2sin(x)

extreme points

2 cos (x) + 2 sin (x)

Maximum (\frac{π}{4} + 2 πn, 22), Minimum (\frac{5 π}{4} + 2 πn, - 22)

Solution steps

Find the critical points:

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

Domain of

2 cos (x) + 2 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

2 cos (x) + 2 sin (x) \Rightarrow y = 22

Maximum (\frac{π}{4} + 2 πn, 22)

Plug the extreme point

x = \frac{5 π}{4} + 2 πn

into

2 cos (x) + 2 sin (x) \Rightarrow y = - 22

Minimum (\frac{5 π}{4} + 2 πn, - 22)

Maximum (\frac{π}{4} + 2 πn, 22), Minimum (\frac{5 π}{4} + 2 πn, - 22)

f (x) = \frac{8}{x ^{2} - 4}

\frac{3 ( x - 7 ) ( x - 6 )}{3 ( x - 7 )}

f (x) = x^{3} + x + 1

f (x) = 40 x - 3 x^{2}

f (x) = - 3 x^{2} - 5 x - 4

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