What is the extreme f(x)=6sin(x)+6cos(x) ?

The extreme f(x)=6sin(x)+6cos(x) is Maximum(pi/4+2pin,6sqrt(2)),Minimum((5pi)/4+2pin,-6sqrt(2))

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extreme f(x)=6sin(x)+6cos(x)

extreme points

f (x) = 6 sin (x) + 6 cos (x)

Maximum (\frac{π}{4} + 2 πn, 62), Minimum (\frac{5 π}{4} + 2 πn, - 62)

Solution steps

Find the critical points:

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

Domain of

6 sin (x) + 6 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

6 sin (x) + 6 cos (x) \Rightarrow y = 62

Maximum (\frac{π}{4} + 2 πn, 62)

Plug the extreme point

x = \frac{5 π}{4} + 2 πn

into

6 sin (x) + 6 cos (x) \Rightarrow y = - 62

Minimum (\frac{5 π}{4} + 2 πn, - 62)

Maximum (\frac{π}{4} + 2 πn, 62), Minimum (\frac{5 π}{4} + 2 πn, - 62)

f (x) = ln (1 - x) + 10 x

f (x) = 10 - ∣ x ∣

f (x) = - \frac{5}{3} x^{3} + 15 x^{2} + 35 x + 10

f (x) = f (x) = 30 + 20 x^{3} - 5 x^{4} - x^{5}

f (x, y) = - 4 x + 15 y

What is the extreme f(x)=6sin(x)+6cos(x) ?
The extreme f(x)=6sin(x)+6cos(x) is Maximum(pi/4+2pin,6sqrt(2)),Minimum((5pi)/4+2pin,-6sqrt(2))