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Popular >

extreme f(x)=x(17-45+2x)(45/2-x)

Solution

extreme points

f (x) = x (17 - 45 + 2 x) (\frac{45}{2} - x)

Solution

Minimum (\frac{73 - 1549}{6}, - \frac{24893 + 1549 1549}{54}), Maximum (\frac{73 + 1549}{6}, \frac{1549 1549 - 24893}{54})

Solution steps

f^{'} (x) = - 6 x^{2} + 146 x - 630

Find intervals:

Decreasing

: - \infty < x < \frac{- 1549 + 73}{6},

Increasing

: \frac{- 1549 + 73}{6} < x < \frac{1549 + 73}{6},

Decreasing

: \frac{1549 + 73}{6} < x < \infty

Plug

x = \frac{73 - 1549}{6}

into

x (17 - 45 + 2 x) (\frac{45}{2} - x) : - \frac{24893 + 1549 1549}{54}

Minimum (\frac{73 - 1549}{6}, - \frac{24893 + 1549 1549}{54})

Plug

x = \frac{73 + 1549}{6}

into

x (17 - 45 + 2 x) (\frac{45}{2} - x) : \frac{1549 1549 - 24893}{54}

Maximum (\frac{73 + 1549}{6}, \frac{1549 1549 - 24893}{54})

Minimum (\frac{73 - 1549}{6}, - \frac{24893 + 1549 1549}{54}), Maximum (\frac{73 + 1549}{6}, \frac{1549 1549 - 24893}{54})

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Frequently Asked Questions (FAQ)

What is the extreme f(x)=x(17-45+2x)(45/2-x) ?
The extreme f(x)=x(17-45+2x)(45/2-x) is