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Popular >

extreme 4h^3-96h^2+527h

Solution

extreme points

4 h^{3} - 96 h^{2} + 527 h

Solution

Maximum (\frac{48 - 723}{6}, - 8 (1009 - 32723) + \frac{73728 - 2063 723}{9}), Minimum (\frac{48 + 723}{6}, - 8 (1009 + 32723) + \frac{73728 + 2063 723}{9})

Solution steps

f^{'} (h) = 12 h^{2} - 192 h + 527

Find intervals:

Increasing

: - \infty < h < - \frac{241}{2 3} + 8,

Decreasing

: - \frac{241}{2 3} + 8 < h < \frac{241}{2 3} + 8,

Increasing

: \frac{241}{2 3} + 8 < h < \infty

Plug

h = \frac{48 - 723}{6}

into

4 h^{3} - 96 h^{2} + 527 h : - 8 (1009 - 32723) + \frac{73728 - 2063 723}{9}

Maximum (\frac{48 - 723}{6}, - 8 (1009 - 32723) + \frac{73728 - 2063 723}{9})

Plug

h = \frac{48 + 723}{6}

into

4 h^{3} - 96 h^{2} + 527 h : - 8 (1009 + 32723) + \frac{73728 + 2063 723}{9}

Minimum (\frac{48 + 723}{6}, - 8 (1009 + 32723) + \frac{73728 + 2063 723}{9})

Maximum (\frac{48 - 723}{6}, - 8 (1009 - 32723) + \frac{73728 - 2063 723}{9}), Minimum (\frac{48 + 723}{6}, - 8 (1009 + 32723) + \frac{73728 + 2063 723}{9})

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Frequently Asked Questions (FAQ)

What is the extreme 4h^3-96h^2+527h ?
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