What is the extreme f(x)=8sin(|x|),-2pi<= x<= 2pi ?

Q: What is the extreme f(x)=8sin(|x|),-2pi<= x<= 2pi ?

The extreme f(x)=8sin(|x|),-2pi<= x<= 2pi is

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Popular >

extreme f(x)=8sin(|x|),-2pi<= x<= 2pi

Solution

extreme points

f (x) = 8 sin (∣ x ∣), - 2 π \leq x \leq 2 π

Solution

Maximum (- 2 π, 0), Minimum (- \frac{3 π}{2}, - 8), Maximum (- \frac{π}{2}, 8), Minimum (0, 0), Maximum (\frac{π}{2}, 8), Minimum (\frac{3 π}{2}, - 8), Maximum (2 π, 0)

Solution steps

Find the critical points:

x = - 2 π, x = - \frac{3 π}{2}, x = - \frac{π}{2}, x = 0, x = \frac{π}{2}, x = \frac{3 π}{2}, x = 2 π

Find intervals:

Decreasing

: - 2 π < x < - \frac{3 π}{2},

Increasing

: - \frac{3 π}{2} < x < - \frac{π}{2},

Decreasing

: - \frac{π}{2} < x < 0,

Increasing

: 0 < x < \frac{π}{2},

Decreasing

: \frac{π}{2} < x < \frac{3 π}{2},

Increasing

: \frac{3 π}{2} < x < 2 π

Plug the extreme point

x = - 2 π

into

8 sin (∣ x ∣) \Rightarrow y = 0

Maximum (- 2 π, 0)

Plug the extreme point

x = - \frac{3 π}{2}

into

8 sin (∣ x ∣) \Rightarrow y = - 8

Minimum (- \frac{3 π}{2}, - 8)

Plug the extreme point

x = - \frac{π}{2}

into

8 sin (∣ x ∣) \Rightarrow y = 8

Maximum (- \frac{π}{2}, 8)

Plug the extreme point

x = 0

into

8 sin (∣ x ∣) \Rightarrow y = 0

Minimum (0, 0)

Plug the extreme point

x = \frac{π}{2}

into

8 sin (∣ x ∣) \Rightarrow y = 8

Maximum (\frac{π}{2}, 8)

Plug the extreme point

x = \frac{3 π}{2}

into

8 sin (∣ x ∣) \Rightarrow y = - 8

Minimum (\frac{3 π}{2}, - 8)

Plug the extreme point

x = 2 π

into

8 sin (∣ x ∣) \Rightarrow y = 0

Maximum (2 π, 0)

Maximum (- 2 π, 0), Minimum (- \frac{3 π}{2}, - 8), Maximum (- \frac{π}{2}, 8), Minimum (0, 0), Maximum (\frac{π}{2}, 8), Minimum (\frac{3 π}{2}, - 8), Maximum (2 π, 0)

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Frequently Asked Questions (FAQ)

What is the extreme f(x)=8sin(|x|),-2pi<= x<= 2pi ?
The extreme f(x)=8sin(|x|),-2pi<= x<= 2pi is