What is the extreme f(x)=2x^3-24x,-4<= x<= 4 ?

The extreme f(x)=2x^3-24x,-4<= x<= 4 is Minimum(-4,-32),Maximum(-2,32),Minimum(2,-32),Maximum(4,32)

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extreme f(x)=2x^3-24x,-4<= x<= 4

extreme

Minimum (- 4, - 32), Maximum (- 2, 32), Minimum (2, - 32), Maximum (4, 32)

Solution steps

Find the critical points:

x = - 4, x = - 2, x = 2, x = 4

Domain of

2 x^{3} - 24 x, - 4 \leq x \leq 4 : - 4 \leq x \leq 4

Find intervals:

Increasing

: - 4 < x < - 2,

Decreasing

: - 2 < x < 2,

Increasing

: 2 < x < 4

Plug the extreme point

x = - 4

into

2 x^{3} - 24 x \Rightarrow y = - 32

Minimum (- 4, - 32)

Plug the extreme point

x = - 2

into

2 x^{3} - 24 x \Rightarrow y = 32

Maximum (- 2, 32)

Plug the extreme point

x = 2

into

2 x^{3} - 24 x \Rightarrow y = - 32

Minimum (2, - 32)

Plug the extreme point

x = 4

into

2 x^{3} - 24 x \Rightarrow y = 32

Maximum (4, 32)

Minimum (- 4, - 32), Maximum (- 2, 32), Minimum (2, - 32), Maximum (4, 32)

What is the extreme f(x)=2x^3-24x,-4<= x<= 4 ?
The extreme f(x)=2x^3-24x,-4<= x<= 4 is Minimum(-4,-32),Maximum(-2,32),Minimum(2,-32),Maximum(4,32)