What is the extreme f(x)=4sin(x)+4cos(x) ?

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

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extreme f(x)=4sin(x)+4cos(x)

extreme points

f (x) = 4 sin (x) + 4 cos (x)

Maximum (\frac{π}{4} + 2 πn, 42), Minimum (\frac{5 π}{4} + 2 πn, - 42)

Solution steps

Find the critical points:

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

Domain of

4 sin (x) + 4 cos (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

4 sin (x) + 4 cos (x) \Rightarrow y = 42

Maximum (\frac{π}{4} + 2 πn, 42)

Plug the extreme point

x = \frac{5 π}{4} + 2 πn

into

4 sin (x) + 4 cos (x) \Rightarrow y = - 42

Minimum (\frac{5 π}{4} + 2 πn, - 42)

Maximum (\frac{π}{4} + 2 πn, 42), Minimum (\frac{5 π}{4} + 2 πn, - 42)

f (x) = x^{2} + 2 y^{2}

f (x) = \frac{6}{x + 7}

f (x) = - 5 x + 3 ln (4 x), (0, 4)

f (x) = x^{2} y - 15 x y^{2} + 12 y

f (x) = x^{3} - 9 x^{2} + 15 x + 3

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