What is the extreme f(x)=6x^{2/3}-x,0<= x<= 216 ?

The extreme f(x)=6x^{2/3}-x,0<= x<= 216 is Minimum(0,0),Maximum(64,32),Minimum(216,0)

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extreme f(x)=6x^{2/3}-x,0<= x<= 216

extreme points

f (x) = 6 x^{\frac{2}{3}} - x, 0 \leq x \leq 216

Minimum (0, 0), Maximum (64, 32), Minimum (216, 0)

Solution steps

Find the critical points:

x = 0, x = 64, x = 216

Domain of

6 x^{\frac{2}{3}} - x, 0 \leq x \leq 216 : 0 \leq x \leq 216

Find intervals:

Increasing

: 0 < x < 64,

Decreasing

: 64 < x < 216

Plug the extreme point

x = 0

into

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

Minimum (0, 0)

Plug the extreme point

x = 64

into

6 x^{\frac{2}{3}} - x \Rightarrow y = 32

Maximum (64, 32)

Plug the extreme point

x = 216

into

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

Minimum (216, 0)

Minimum (0, 0), Maximum (64, 32), Minimum (216, 0)

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

7 + 4 x^{2} - x^{4}

f (x) = 1.3 t e^{- 2.9 t}

y = x \cdot 1 + x^{2}

f (x, y) = (x - 1)^{3} + (y - 2)^{3} - 3 x - 3 y

What is the extreme f(x)=6x^{2/3}-x,0<= x<= 216 ?
The extreme f(x)=6x^{2/3}-x,0<= x<= 216 is Minimum(0,0),Maximum(64,32),Minimum(216,0)