What is the extreme \sqrt[3]{t}(8-t) ?

The extreme \sqrt[3]{t}(8-t) is Maximum(2,6\sqrt[3]{2})

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extreme \sqrt[3]{t}(8-t)

extreme points

3 t (8 - t)

Maximum (2, 632)

Solution steps

Find the critical points:

t = 0, t = 2

Domain of

3 t (8 - t) : - \infty < t < \infty

Find intervals:

Increasing

: - \infty < t < 0,

Increasing

: 0 < t < 2,

Decreasing

: 2 < t < \infty

Plug the extreme point

x = 2

into

3 t (8 - t) \Rightarrow y = 632

Maximum (2, 632)

f (x) = - x^{2} + 50 ln (x)

f (x) = - 69.7 x^{2} + 625.6 x

f (x) = \frac{1}{2} (x + 4)^{2} + 6

f (x) = - 0.3 x^{2} + 2.4 x + 98.8

\frac{2}{x + 3} - 1

What is the extreme \sqrt[3]{t}(8-t) ?
The extreme \sqrt[3]{t}(8-t) is Maximum(2,6\sqrt[3]{2})