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Popular >

extreme f(x)=x(sqrt((39900-x)/5))

Solution

extreme points

f (x) = x (\frac{39900 - x}{5})

Solution

Maximum (\frac{319200 - 31920 0 ^{2} - 3990 0 ^{2} \cdot 48}{6}, \frac{( 319200 - 31920 0 ^{2} - 3990 0 ^{2} \cdot 48 ) 31920 0 ^{2} - 3990 0 ^{2} \cdot 48 - 79800}{6 30}), Minimum (39900, 0)

Solution steps

f^{'} (x) = \frac{39900 - x}{5} - \frac{x}{2 5 39900 - x}

Find intervals:

Increasing

: - \infty < x < \frac{- 31920 0 ^{2} - 76416480000 + 319200}{6},

Decreasing

: \frac{- 31920 0 ^{2} - 76416480000 + 319200}{6} < x < 39900

Plug

x = \frac{319200 - 31920 0 ^{2} - 3990 0 ^{2} \cdot 48}{6}

into

x \frac{39900 - x}{5} : \frac{( 319200 - 31920 0 ^{2} - 3990 0 ^{2} \cdot 48 ) 31920 0 ^{2} - 3990 0 ^{2} \cdot 48 - 79800}{6 30}

Maximum (\frac{319200 - 31920 0 ^{2} - 3990 0 ^{2} \cdot 48}{6}, \frac{( 319200 - 31920 0 ^{2} - 3990 0 ^{2} \cdot 48 ) 31920 0 ^{2} - 3990 0 ^{2} \cdot 48 - 79800}{6 30})

Plug

x = 39900

into

x \frac{39900 - x}{5} : 0

Minimum (39900, 0)

Maximum (\frac{319200 - 31920 0 ^{2} - 3990 0 ^{2} \cdot 48}{6}, \frac{( 319200 - 31920 0 ^{2} - 3990 0 ^{2} \cdot 48 ) 31920 0 ^{2} - 3990 0 ^{2} \cdot 48 - 79800}{6 30}), Minimum (39900, 0)

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Frequently Asked Questions (FAQ)

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