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

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)

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