What is the extreme f(x)=16sin(2x),-2pi<= x<= 2pi ?

Q: What is the extreme f(x)=16sin(2x),-2pi<= x<= 2pi ?

The extreme f(x)=16sin(2x),-2pi<= x<= 2pi is

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Popular >

extreme f(x)=16sin(2x),-2pi<= x<= 2pi

Solution

extreme points

f (x) = 16 sin (2 x), - 2 π \leq x \leq 2 π

Solution

Minimum (- 2 π, 0), Maximum (- \frac{7 π}{4}, 16), Minimum (- \frac{5 π}{4}, - 16), Maximum (- \frac{3 π}{4}, 16), Minimum (- \frac{π}{4}, - 16), Maximum (\frac{π}{4}, 16), Minimum (\frac{3 π}{4}, - 16), Maximum (\frac{5 π}{4}, 16), Minimum (\frac{7 π}{4}, - 16), Maximum (2 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 = \frac{5 π}{4}, x = \frac{7 π}{4}, x = 2 π

Domain of

16 sin (2 x), - 2 π \leq x \leq 2 π : - 2 π \leq x \leq 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 = - 2 π

into

16 sin (2 x) \Rightarrow y = 0

Minimum (- 2 π, 0)

Plug the extreme point

x = - \frac{7 π}{4}

into

16 sin (2 x) \Rightarrow y = 16

Maximum (- \frac{7 π}{4}, 16)

Plug the extreme point

x = - \frac{5 π}{4}

into

16 sin (2 x) \Rightarrow y = - 16

Minimum (- \frac{5 π}{4}, - 16)

Plug the extreme point

x = - \frac{3 π}{4}

into

16 sin (2 x) \Rightarrow y = 16

Maximum (- \frac{3 π}{4}, 16)

Plug the extreme point

x = - \frac{π}{4}

into

16 sin (2 x) \Rightarrow y = - 16

Minimum (- \frac{π}{4}, - 16)

Plug the extreme point

x = \frac{π}{4}

into

16 sin (2 x) \Rightarrow y = 16

Maximum (\frac{π}{4}, 16)

Plug the extreme point

x = \frac{3 π}{4}

into

16 sin (2 x) \Rightarrow y = - 16

Minimum (\frac{3 π}{4}, - 16)

Plug the extreme point

x = \frac{5 π}{4}

into

16 sin (2 x) \Rightarrow y = 16

Maximum (\frac{5 π}{4}, 16)

Plug the extreme point

x = \frac{7 π}{4}

into

16 sin (2 x) \Rightarrow y = - 16

Minimum (\frac{7 π}{4}, - 16)

Plug the extreme point

x = 2 π

into

16 sin (2 x) \Rightarrow y = 0

Maximum (2 π, 0)

Minimum (- 2 π, 0), Maximum (- \frac{7 π}{4}, 16), Minimum (- \frac{5 π}{4}, - 16), Maximum (- \frac{3 π}{4}, 16), Minimum (- \frac{π}{4}, - 16), Maximum (\frac{π}{4}, 16), Minimum (\frac{3 π}{4}, - 16), Maximum (\frac{5 π}{4}, 16), Minimum (\frac{7 π}{4}, - 16), Maximum (2 π, 0)

Graph

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Frequently Asked Questions (FAQ)

What is the extreme f(x)=16sin(2x),-2pi<= x<= 2pi ?
The extreme f(x)=16sin(2x),-2pi<= x<= 2pi is