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Popular >

extreme f(x)=(2x^2-5x)/(2x+7)

Solution

extreme points

f (x) = \frac{2 x ^{2} - 5 x}{2 x + 7}

Solution

Maximum (- \frac{7 + 2 21}{2}, - \frac{84 + 19 21}{2 21}), Minimum (\frac{- 7 + 2 21}{2}, \frac{84 - 19 21}{2 21})

Solution steps

f^{'} (x) = \frac{4 x ^{2} + 28 x - 35}{( 2 x + 7 ) ^{2}}

Find intervals:

Increasing

: - \infty < x < - \frac{7 + 2 21}{2},

Decreasing

: - \frac{7 + 2 21}{2} < x < - \frac{7}{2},

Decreasing

: - \frac{7}{2} < x < \frac{2 21 - 7}{2},

Increasing

: \frac{2 21 - 7}{2} < x < \infty

Plug

x = - \frac{7 + 2 21}{2}

into

\frac{2 x ^{2} - 5 x}{2 x + 7} : - \frac{84 + 19 21}{2 21}

Maximum (- \frac{7 + 2 21}{2}, - \frac{84 + 19 21}{2 21})

Plug

x = \frac{- 7 + 2 21}{2}

into

\frac{2 x ^{2} - 5 x}{2 x + 7} : \frac{84 - 19 21}{2 21}

Minimum (\frac{- 7 + 2 21}{2}, \frac{84 - 19 21}{2 21})

Maximum (- \frac{7 + 2 21}{2}, - \frac{84 + 19 21}{2 21}), Minimum (\frac{- 7 + 2 21}{2}, \frac{84 - 19 21}{2 21})

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extreme f(x)=-1/6000 x+85/6 extreme points

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Frequently Asked Questions (FAQ)

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