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

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

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

extreme points

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

Maximum (- 1, 1), Minimum (0, 0), Maximum (2, 2^{\frac{2}{3}})

Solution steps

Find the critical points:

x = - 1, x = 0, x = 2

Domain of

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

Find intervals:

Decreasing

: - 1 < x < 0,

Increasing

: 0 < x < 2

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 = 2

into

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

Maximum (2, 2^{\frac{2}{3}})

Maximum (- 1, 1), Minimum (0, 0), Maximum (2, 2^{\frac{2}{3}})

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