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

The extreme 3x^{2/3}-2x,-1<= x<= 1 is Maximum(-1,5),Minimum(0,0),Maximum(1,1)

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

extreme points

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

Maximum (- 1, 5), Minimum (0, 0), Maximum (1, 1)

Solution steps

Find the critical points:

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

Domain of

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

Find intervals:

Decreasing

: - 1 < x < 0,

Increasing

: 0 < x < 1

Plug the extreme point

x = - 1

into

3 x^{\frac{2}{3}} - 2 x \Rightarrow y = 5

Maximum (- 1, 5)

Plug the extreme point

x = 0

into

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

Minimum (0, 0)

Plug the extreme point

x = 1

into

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

Maximum (1, 1)

Maximum (- 1, 5), Minimum (0, 0), Maximum (1, 1)

f (x) = - 25 (x - 9)^{2} + 200

f (x) = - x^{3} + 3 x - 10

uv

y = 4 x + 4 sin (x)

f (x, y) = x^{3} + y^{3} - 147 x - 75 y - 10

What is the extreme 3x^{2/3}-2x,-1<= x<= 1 ?
The extreme 3x^{2/3}-2x,-1<= x<= 1 is Maximum(-1,5),Minimum(0,0),Maximum(1,1)