What is the extreme f(x)=4x^{3/4}-x,0<= x<= 256 ?

The extreme f(x)=4x^{3/4}-x,0<= x<= 256 is Minimum(0,0),Maximum(81,27),Minimum(256,0)

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extreme f(x)=4x^{3/4}-x,0<= x<= 256

extreme points

f (x) = 4 x^{\frac{3}{4}} - x, 0 \leq x \leq 256

Minimum (0, 0), Maximum (81, 27), Minimum (256, 0)

Solution steps

Find the critical points:

x = 0, x = 81, x = 256

Domain of

4 x^{\frac{3}{4}} - x, 0 \leq x \leq 256 : 0 \leq x \leq 256

Find intervals:

Increasing

: 0 < x < 81,

Decreasing

: 81 < x < 256

Plug the extreme point

x = 0

into

4 x^{\frac{3}{4}} - x \Rightarrow y = 0

Minimum (0, 0)

Plug the extreme point

x = 81

into

4 x^{\frac{3}{4}} - x \Rightarrow y = 27

Maximum (81, 27)

Plug the extreme point

x = 256

into

4 x^{\frac{3}{4}} - x \Rightarrow y = 0

Minimum (256, 0)

Minimum (0, 0), Maximum (81, 27), Minimum (256, 0)

- x^{3} + 6 x^{2} + 15 x + 4

f (x) = x^{2} - 5 x - 1

f (x) = x x + 8

f (x) = \frac{x + 2}{x ^{2} - 3 x - 10}

f (x) = (x^{2} - 2 x) e^{- x}

What is the extreme f(x)=4x^{3/4}-x,0<= x<= 256 ?
The extreme f(x)=4x^{3/4}-x,0<= x<= 256 is Minimum(0,0),Maximum(81,27),Minimum(256,0)