What is the extreme f(x)=10sin(2x),(-2pi,2pi) ?

The extreme f(x)=10sin(2x),(-2pi,2pi) is

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Popular >

extreme f(x)=10sin(2x),(-2pi,2pi)

Solution

extreme points

f (x) = 10 sin (2 x), (- 2 π, 2 π)

Solution

Maximum (- \frac{7 π}{4}, 10), Minimum (- \frac{5 π}{4}, - 10), Maximum (- \frac{3 π}{4}, 10), Minimum (- \frac{π}{4}, - 10), Maximum (\frac{π}{4}, 10), Minimum (\frac{3 π}{4}, - 10), Maximum (\frac{5 π}{4}, 10), Minimum (\frac{7 π}{4}, - 10)

Solution steps

Find the critical points:

x = - \frac{7 π}{4}, x = - \frac{5 π}{4}, x = - \frac{3 π}{4}, x = - \frac{π}{4}, x = \frac{π}{4}, x = \frac{3 π}{4}, x = \frac{5 π}{4}, x = \frac{7 π}{4}

Domain of

10 sin (2 x), (- 2 π, 2 π) : - 2 π < x < 2 π

Find intervals:

Increasing

: - 2 π < x < - \frac{7 π}{4},

Decreasing

: - \frac{7 π}{4} < x < - \frac{5 π}{4},

Increasing

: - \frac{5 π}{4} < x < - \frac{3 π}{4},

Decreasing

: - \frac{3 π}{4} < x < - \frac{π}{4},

Increasing

: - \frac{π}{4} < x < \frac{π}{4},

Decreasing

: \frac{π}{4} < x < \frac{3 π}{4},

Increasing

: \frac{3 π}{4} < x < \frac{5 π}{4},

Decreasing

: \frac{5 π}{4} < x < \frac{7 π}{4},

Increasing

: \frac{7 π}{4} < x < 2 π

Plug the extreme point

x = - \frac{7 π}{4}

into

10 sin (2 x) \Rightarrow y = 10

Maximum (- \frac{7 π}{4}, 10)

Plug the extreme point

x = - \frac{5 π}{4}

into

10 sin (2 x) \Rightarrow y = - 10

Minimum (- \frac{5 π}{4}, - 10)

Plug the extreme point

x = - \frac{3 π}{4}

into

10 sin (2 x) \Rightarrow y = 10

Maximum (- \frac{3 π}{4}, 10)

Plug the extreme point

x = - \frac{π}{4}

into

10 sin (2 x) \Rightarrow y = - 10

Minimum (- \frac{π}{4}, - 10)

Plug the extreme point

x = \frac{π}{4}

into

10 sin (2 x) \Rightarrow y = 10

Maximum (\frac{π}{4}, 10)

Plug the extreme point

x = \frac{3 π}{4}

into

10 sin (2 x) \Rightarrow y = - 10

Minimum (\frac{3 π}{4}, - 10)

Plug the extreme point

x = \frac{5 π}{4}

into

10 sin (2 x) \Rightarrow y = 10

Maximum (\frac{5 π}{4}, 10)

Plug the extreme point

x = \frac{7 π}{4}

into

10 sin (2 x) \Rightarrow y = - 10

Minimum (\frac{7 π}{4}, - 10)

Maximum (- \frac{7 π}{4}, 10), Minimum (- \frac{5 π}{4}, - 10), Maximum (- \frac{3 π}{4}, 10), Minimum (- \frac{π}{4}, - 10), Maximum (\frac{π}{4}, 10), Minimum (\frac{3 π}{4}, - 10), Maximum (\frac{5 π}{4}, 10), Minimum (\frac{7 π}{4}, - 10)

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Frequently Asked Questions (FAQ)

What is the extreme f(x)=10sin(2x),(-2pi,2pi) ?
The extreme f(x)=10sin(2x),(-2pi,2pi) is