What is the extreme 4sin(2x),-2pi<= x<= pi ?

Q: What is the extreme 4sin(2x),-2pi<= x<= pi ?

The extreme 4sin(2x),-2pi<= x<= pi is

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Popular >

extreme 4sin(2x),-2pi<= x<= pi

Solution

extreme points

4 sin (2 x), - 2 π \leq x \leq π

Solution

Minimum (- 2 π, 0), Maximum (- \frac{7 π}{4}, 4), Minimum (- \frac{5 π}{4}, - 4), Maximum (- \frac{3 π}{4}, 4), Minimum (- \frac{π}{4}, - 4), Maximum (\frac{π}{4}, 4), Minimum (\frac{3 π}{4}, - 4), Maximum (π, 0)

Solution steps

Find the critical points:

x = - 2 π, 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 = π

Domain of

4 sin (2 x), - 2 π \leq x \leq π : - 2 π \leq x \leq 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 < π

Plug the extreme point

x = - 2 π

into

4 sin (2 x) \Rightarrow y = 0

Minimum (- 2 π, 0)

Plug the extreme point

x = - \frac{7 π}{4}

into

4 sin (2 x) \Rightarrow y = 4

Maximum (- \frac{7 π}{4}, 4)

Plug the extreme point

x = - \frac{5 π}{4}

into

4 sin (2 x) \Rightarrow y = - 4

Minimum (- \frac{5 π}{4}, - 4)

Plug the extreme point

x = - \frac{3 π}{4}

into

4 sin (2 x) \Rightarrow y = 4

Maximum (- \frac{3 π}{4}, 4)

Plug the extreme point

x = - \frac{π}{4}

into

4 sin (2 x) \Rightarrow y = - 4

Minimum (- \frac{π}{4}, - 4)

Plug the extreme point

x = \frac{π}{4}

into

4 sin (2 x) \Rightarrow y = 4

Maximum (\frac{π}{4}, 4)

Plug the extreme point

x = \frac{3 π}{4}

into

4 sin (2 x) \Rightarrow y = - 4

Minimum (\frac{3 π}{4}, - 4)

Plug the extreme point

x = π

into

4 sin (2 x) \Rightarrow y = 0

Maximum (π, 0)

Minimum (- 2 π, 0), Maximum (- \frac{7 π}{4}, 4), Minimum (- \frac{5 π}{4}, - 4), Maximum (- \frac{3 π}{4}, 4), Minimum (- \frac{π}{4}, - 4), Maximum (\frac{π}{4}, 4), Minimum (\frac{3 π}{4}, - 4), Maximum (π, 0)

Graph

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Frequently Asked Questions (FAQ)

What is the extreme 4sin(2x),-2pi<= x<= pi ?
The extreme 4sin(2x),-2pi<= x<= pi is