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

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

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

extreme points

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

Minimum (- 1, - 3), Maximum (0, 0), Minimum (1, - 3)

Solution steps

Find the critical points:

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

Domain of

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

Find intervals:

Increasing

: - 1 < x < 0,

Decreasing

: 0 < x < 1

Plug the extreme point

x = - 1

into

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

Minimum (- 1, - 3)

Plug the extreme point

x = 0

into

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

Maximum (0, 0)

Plug the extreme point

x = 1

into

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

Minimum (1, - 3)

Minimum (- 1, - 3), Maximum (0, 0), Minimum (1, - 3)

f (x) = x^{3} + 3 x^{2} - 24 x, - 1 \leq x \leq 3

f (x, y) = x^{2} + x y + y^{2} - 2 x - y

f (x, y) = 6 x y - 4 x^{3} - 3 y^{2}

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

f (x) = 3 x^{3} - x

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