What is the extreme \sqrt[3]{x}(28-x) ?

The extreme \sqrt[3]{x}(28-x) is Maximum(7,21\sqrt[3]{7})

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extreme \sqrt[3]{x}(28-x)

extreme points

3 x (28 - x)

Maximum (7, 2137)

Solution steps

Find the critical points:

x = 0, x = 7

Domain of

3 x (28 - x) : - \infty < x < \infty

Find intervals:

Increasing

: - \infty < x < 0,

Increasing

: 0 < x < 7,

Decreasing

: 7 < x < \infty

Plug the extreme point

x = 7

into

3 x (28 - x) \Rightarrow y = 2137

Maximum (7, 2137)

f (x) = x^{3} + 15 x - 9

f (x) = x^{3} - 2 x^{2} - 15 x + 52.2

f (x) = 3 x^{2} - 5 y^{2} - 255 x + 70 y + 23

f (x) = 5 x e^{- x} + 9

f (x, y) = 3 x^{2} + 2 y^{2} - 4 y + 10 y

What is the extreme \sqrt[3]{x}(28-x) ?
The extreme \sqrt[3]{x}(28-x) is Maximum(7,21\sqrt[3]{7})