What is the extreme f(x)=-2x+6x^{2/3},-8<= x<= 4.5 ?

The extreme f(x)=-2x+6x^{2/3},-8<= x<= 4.5 is Maximum(-8,40),Minimum(0,0),Maximum(4.5,7.35408…)

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extreme f(x)=-2x+6x^{2/3},-8<= x<= 4.5

extreme

Maximum (- 8, 40), Minimum (0, 0), Maximum (4.5, 7.35408 \dots)

Solution steps

Find the critical points:

x = - 8, x = 0, x = 4.5

Domain of

- 2 x + 6 x^{\frac{2}{3}}, - 8 \leq x \leq 4.5 : - 8 \leq x \leq 4.5

Find intervals:

Decreasing

: - 8 < x < 0,

Increasing

: 0 < x < 4.5

Plug the extreme point

x = - 8

into

- 2 x + 6 x^{\frac{2}{3}} \Rightarrow y = 40

Maximum (- 8, 40)

Plug the extreme point

x = 0

into

- 2 x + 6 x^{\frac{2}{3}} \Rightarrow y = 0

Minimum (0, 0)

Plug the extreme point

x = 4.5

into

- 2 x + 6 x^{\frac{2}{3}} \Rightarrow y = 7.35408 \dots

Maximum (4.5, 7.35408 \dots)

Maximum (- 8, 40), Minimum (0, 0), Maximum (4.5, 7.35408 \dots)

What is the extreme f(x)=-2x+6x^{2/3},-8<= x<= 4.5 ?
The extreme f(x)=-2x+6x^{2/3},-8<= x<= 4.5 is Maximum(-8,40),Minimum(0,0),Maximum(4.5,7.35408…)