What is the extreme f(x)=x^{2/3},-1<= x<= 27 ?

The extreme f(x)=x^{2/3},-1<= x<= 27 is Maximum(-1,1),Minimum(0,0),Maximum(27,9)

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extreme f(x)=x^{2/3},-1<= x<= 27

extreme points

f (x) = x^{\frac{2}{3}}, - 1 \leq x \leq 27

Maximum (- 1, 1), Minimum (0, 0), Maximum (27, 9)

Solution steps

Find the critical points:

x = - 1, x = 0, x = 27

Domain of

x^{\frac{2}{3}}, - 1 \leq x \leq 27 : - 1 \leq x \leq 27

Find intervals:

Decreasing

: - 1 < x < 0,

Increasing

: 0 < x < 27

Plug the extreme point

x = - 1

into

x^{\frac{2}{3}} \Rightarrow y = 1

Maximum (- 1, 1)

Plug the extreme point

x = 0

into

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

Minimum (0, 0)

Plug the extreme point

x = 27

into

x^{\frac{2}{3}} \Rightarrow y = 9

Maximum (27, 9)

Maximum (- 1, 1), Minimum (0, 0), Maximum (27, 9)

f (x) = \frac{1}{4} x^{4} - 2 x^{3} + 4

f (x) = \frac{1}{4} x^{4} - 2 x^{3} + 1

y = \frac{x}{x ^{2} + 4}

y = x (x - 1)^{5}

f (x) = x^{3} + 6 x^{2} - 6

What is the extreme f(x)=x^{2/3},-1<= x<= 27 ?
The extreme f(x)=x^{2/3},-1<= x<= 27 is Maximum(-1,1),Minimum(0,0),Maximum(27,9)