What is the extreme f(x)=sin(x),-5<= x<= 6 ?

Q: What is the extreme f(x)=sin(x),-5<= x<= 6 ?

The extreme f(x)=sin(x),-5<= x<= 6 is

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Popular >

extreme f(x)=sin(x),-5<= x<= 6

Solution

extreme points

f (x) = sin (x), - 5 \leq x \leq 6

Solution

Minimum (- 5, - sin (5)), Maximum (- \frac{3 π}{2}, 1), Minimum (- \frac{π}{2}, - 1), Maximum (\frac{π}{2}, 1), Minimum (\frac{3 π}{2}, - 1), Maximum (6, sin (6))

Solution steps

Find the critical points:

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

Domain of

sin (x), - 5 \leq x \leq 6 : - 5 \leq x \leq 6

Find intervals:

Increasing

: - 5 < x < - \frac{3 π}{2},

Decreasing

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

Increasing

: - \frac{π}{2} < x < \frac{π}{2},

Decreasing

: \frac{π}{2} < x < \frac{3 π}{2},

Increasing

: \frac{3 π}{2} < x < 6

Plug the extreme point

x = - 5

into

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

Minimum (- 5, - sin (5))

Plug the extreme point

x = - \frac{3 π}{2}

into

sin (x) \Rightarrow y = 1

Maximum (- \frac{3 π}{2}, 1)

Plug the extreme point

x = - \frac{π}{2}

into

sin (x) \Rightarrow y = - 1

Minimum (- \frac{π}{2}, - 1)

Plug the extreme point

x = \frac{π}{2}

into

sin (x) \Rightarrow y = 1

Maximum (\frac{π}{2}, 1)

Plug the extreme point

x = \frac{3 π}{2}

into

sin (x) \Rightarrow y = - 1

Minimum (\frac{3 π}{2}, - 1)

Plug the extreme point

x = 6

into

sin (x) \Rightarrow y = sin (6)

Maximum (6, sin (6))

Minimum (- 5, - sin (5)), Maximum (- \frac{3 π}{2}, 1), Minimum (- \frac{π}{2}, - 1), Maximum (\frac{π}{2}, 1), Minimum (\frac{3 π}{2}, - 1), Maximum (6, sin (6))

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Frequently Asked Questions (FAQ)

What is the extreme f(x)=sin(x),-5<= x<= 6 ?
The extreme f(x)=sin(x),-5<= x<= 6 is