What is the extreme f(x)=5sin(3x)-5,(0,2pi) ?

The extreme f(x)=5sin(3x)-5,(0,2pi) is

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Popular >

extreme f(x)=5sin(3x)-5,(0,2pi)

Solution

extreme points

f (x) = 5 sin (3 x) - 5, (0, 2 π)

Solution

Maximum (\frac{π}{6}, 0), Minimum (\frac{π}{2}, - 10), Maximum (\frac{5 π}{6}, 0), Minimum (\frac{7 π}{6}, - 10), Maximum (\frac{3 π}{2}, 0), Minimum (\frac{11 π}{6}, - 10)

Solution steps

Find the critical points:

x = \frac{π}{6}, x = \frac{π}{2}, x = \frac{5 π}{6}, x = \frac{7 π}{6}, x = \frac{3 π}{2}, x = \frac{11 π}{6}

Domain of

5 sin (3 x) - 5, (0, 2 π) : 0 < x < 2 π

Find intervals:

Increasing

: 0 < x < \frac{π}{6},

Decreasing

: \frac{π}{6} < x < \frac{π}{2},

Increasing

: \frac{π}{2} < x < \frac{5 π}{6},

Decreasing

: \frac{5 π}{6} < x < \frac{7 π}{6},

Increasing

: \frac{7 π}{6} < x < \frac{3 π}{2},

Decreasing

: \frac{3 π}{2} < x < \frac{11 π}{6},

Increasing

: \frac{11 π}{6} < x < 2 π

Plug the extreme point

x = \frac{π}{6}

into

5 sin (3 x) - 5 \Rightarrow y = 0

Maximum (\frac{π}{6}, 0)

Plug the extreme point

x = \frac{π}{2}

into

5 sin (3 x) - 5 \Rightarrow y = - 10

Minimum (\frac{π}{2}, - 10)

Plug the extreme point

x = \frac{5 π}{6}

into

5 sin (3 x) - 5 \Rightarrow y = 0

Maximum (\frac{5 π}{6}, 0)

Plug the extreme point

x = \frac{7 π}{6}

into

5 sin (3 x) - 5 \Rightarrow y = - 10

Minimum (\frac{7 π}{6}, - 10)

Plug the extreme point

x = \frac{3 π}{2}

into

5 sin (3 x) - 5 \Rightarrow y = 0

Maximum (\frac{3 π}{2}, 0)

Plug the extreme point

x = \frac{11 π}{6}

into

5 sin (3 x) - 5 \Rightarrow y = - 10

Minimum (\frac{11 π}{6}, - 10)

Maximum (\frac{π}{6}, 0), Minimum (\frac{π}{2}, - 10), Maximum (\frac{5 π}{6}, 0), Minimum (\frac{7 π}{6}, - 10), Maximum (\frac{3 π}{2}, 0), Minimum (\frac{11 π}{6}, - 10)

Graph

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Frequently Asked Questions (FAQ)

What is the extreme f(x)=5sin(3x)-5,(0,2pi) ?
The extreme f(x)=5sin(3x)-5,(0,2pi) is