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Popular >

extreme f(x)=x(22-37+2x)(37/2-x)

Solution

extreme points

f (x) = x (22 - 37 + 2 x) (\frac{37}{2} - x)

Solution

Minimum (\frac{52 - 1039}{6}, \frac{10738 - 1039 1039}{54}), Maximum (\frac{52 + 1039}{6}, \frac{1039 1039 + 10738}{54})

Solution steps

f^{'} (x) = - 6 x^{2} + 104 x - \frac{555}{2}

Find intervals:

Decreasing

: - \infty < x < - \frac{1039}{6} + \frac{26}{3},

Increasing

: - \frac{1039}{6} + \frac{26}{3} < x < \frac{1039}{6} + \frac{26}{3},

Decreasing

: \frac{1039}{6} + \frac{26}{3} < x < \infty

Plug

x = \frac{52 - 1039}{6}

into

x (22 - 37 + 2 x) (\frac{37}{2} - x) : \frac{10738 - 1039 1039}{54}

Minimum (\frac{52 - 1039}{6}, \frac{10738 - 1039 1039}{54})

Plug

x = \frac{52 + 1039}{6}

into

x (22 - 37 + 2 x) (\frac{37}{2} - x) : \frac{1039 1039 + 10738}{54}

Maximum (\frac{52 + 1039}{6}, \frac{1039 1039 + 10738}{54})

Minimum (\frac{52 - 1039}{6}, \frac{10738 - 1039 1039}{54}), Maximum (\frac{52 + 1039}{6}, \frac{1039 1039 + 10738}{54})

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Frequently Asked Questions (FAQ)

What is the extreme f(x)=x(22-37+2x)(37/2-x) ?
The extreme f(x)=x(22-37+2x)(37/2-x) is