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Popular Functions >

extreme |x^4-4x^2-2|,-2<= x<= 2

Solution

extreme

Solution

Minimum (- 2, 2), Maximum (- 2, 6), Minimum (0, 2), Maximum (2, 6), Minimum (2, 2)

Solution steps

Find the critical points:

x = - 2, x = - 2, x = 0, x = 2, x = 2

Find intervals:

Increasing

: - 2 < x < - 2,

Decreasing

: - 2 < x < 0,

Increasing

: 0 < x < 2,

Decreasing

: 2 < x < 2

Plug the extreme point

x = - 2

into

x^{4} - 4 x^{2} - 2 \Rightarrow y = 2

Minimum (- 2, 2)

Plug the extreme point

x = - 2

into

x^{4} - 4 x^{2} - 2 \Rightarrow y = 6

Maximum (- 2, 6)

Plug the extreme point

x = 0

into

x^{4} - 4 x^{2} - 2 \Rightarrow y = 2

Minimum (0, 2)

Plug the extreme point

x = 2

into

x^{4} - 4 x^{2} - 2 \Rightarrow y = 6

Maximum (2, 6)

Plug the extreme point

x = 2

into

x^{4} - 4 x^{2} - 2 \Rightarrow y = 2

Minimum (2, 2)

Minimum (- 2, 2), Maximum (- 2, 6), Minimum (0, 2), Maximum (2, 6), Minimum (2, 2)

Graph

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