What is the extreme f(x)=3sin(x)+3cos(x),(0,2pi) ?

The extreme f(x)=3sin(x)+3cos(x),(0,2pi) is Maximum(pi/4 ,3sqrt(2)),Minimum((5pi)/4 ,-3sqrt(2))

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extreme f(x)=3sin(x)+3cos(x),(0,2pi)

extreme points

f (x) = 3 sin (x) + 3 cos (x), (0, 2 π)

Maximum (\frac{π}{4}, 32), Minimum (\frac{5 π}{4}, - 32)

Solution steps

Find the critical points:

x = \frac{π}{4}, x = \frac{5 π}{4}

Domain of

3 sin (x) + 3 cos (x), (0, 2 π) : 0 < x < 2 π

Find intervals:

Increasing

: 0 < x < \frac{π}{4},

Decreasing

: \frac{π}{4} < x < \frac{5 π}{4},

Increasing

: \frac{5 π}{4} < x < 2 π

Plug the extreme point

x = \frac{π}{4}

into

3 sin (x) + 3 cos (x) \Rightarrow y = 32

Maximum (\frac{π}{4}, 32)

Plug the extreme point

x = \frac{5 π}{4}

into

3 sin (x) + 3 cos (x) \Rightarrow y = - 32

Minimum (\frac{5 π}{4}, - 32)

Maximum (\frac{π}{4}, 32), Minimum (\frac{5 π}{4}, - 32)

f (x) = - \frac{5}{2} sin (\frac{1}{2} x)

f (x) = x^{2} + 7 x - 1

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

5 x^{\frac{2}{3}} - x^{\frac{1}{3}}

2 sin^{2} (x)

What is the extreme f(x)=3sin(x)+3cos(x),(0,2pi) ?
The extreme f(x)=3sin(x)+3cos(x),(0,2pi) is Maximum(pi/4 ,3sqrt(2)),Minimum((5pi)/4 ,-3sqrt(2))