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Popular >

extreme f(x)=x(25-37+2x)(37/2-x)

Solution

extreme points

f (x) = x (25 - 37 + 2 x) (\frac{37}{2} - x)

Solution

Minimum (\frac{49 - 1069}{6}, \frac{19747 - 1069 1069}{54}), Maximum (\frac{49 + 1069}{6}, \frac{1069 1069 + 19747}{54})

Solution steps

f^{'} (x) = - 6 x^{2} + 98 x - 222

Find intervals:

Decreasing

: - \infty < x < \frac{- 1069 + 49}{6},

Increasing

: \frac{- 1069 + 49}{6} < x < \frac{1069 + 49}{6},

Decreasing

: \frac{1069 + 49}{6} < x < \infty

Plug

x = \frac{49 - 1069}{6}

into

x (25 - 37 + 2 x) (\frac{37}{2} - x) : \frac{19747 - 1069 1069}{54}

Minimum (\frac{49 - 1069}{6}, \frac{19747 - 1069 1069}{54})

Plug

x = \frac{49 + 1069}{6}

into

x (25 - 37 + 2 x) (\frac{37}{2} - x) : \frac{1069 1069 + 19747}{54}

Maximum (\frac{49 + 1069}{6}, \frac{1069 1069 + 19747}{54})

Minimum (\frac{49 - 1069}{6}, \frac{19747 - 1069 1069}{54}), Maximum (\frac{49 + 1069}{6}, \frac{1069 1069 + 19747}{54})

Graph

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Frequently Asked Questions (FAQ)

What is the extreme f(x)=x(25-37+2x)(37/2-x) ?
The extreme f(x)=x(25-37+2x)(37/2-x) is