What is the extreme f(x)=2x^{2/3},-27<= x<= 27 ?

The extreme f(x)=2x^{2/3},-27<= x<= 27 is Maximum(-27,18),Minimum(0,0),Maximum(27,18)

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extreme f(x)=2x^{2/3},-27<= x<= 27

extreme points

f (x) = 2 x^{\frac{2}{3}}, - 27 \leq x \leq 27

Maximum (- 27, 18), Minimum (0, 0), Maximum (27, 18)

Solution steps

Find the critical points:

x = - 27, x = 0, x = 27

Domain of

2 x^{\frac{2}{3}}, - 27 \leq x \leq 27 : - 27 \leq x \leq 27

Find intervals:

Decreasing

: - 27 < x < 0,

Increasing

: 0 < x < 27

Plug the extreme point

x = - 27

into

2 x^{\frac{2}{3}} \Rightarrow y = 18

Maximum (- 27, 18)

Plug the extreme point

x = 0

into

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

Minimum (0, 0)

Plug the extreme point

x = 27

into

2 x^{\frac{2}{3}} \Rightarrow y = 18

Maximum (27, 18)

Maximum (- 27, 18), Minimum (0, 0), Maximum (27, 18)

What is the extreme f(x)=2x^{2/3},-27<= x<= 27 ?
The extreme f(x)=2x^{2/3},-27<= x<= 27 is Maximum(-27,18),Minimum(0,0),Maximum(27,18)