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Popular >

extreme f(x)=x(15-43+2x)(43/2-x)

Solution

extreme points

f (x) = x (15 - 43 + 2 x) (\frac{43}{2} - x)

Solution

Minimum (\frac{71 - 1429}{6}, - \frac{26767 + 1429 1429}{54}), Maximum (\frac{71 + 1429}{6}, \frac{1429 1429 - 26767}{54})

Solution steps

f^{'} (x) = - 6 x^{2} + 142 x - 602

Find intervals:

Decreasing

: - \infty < x < \frac{- 1429 + 71}{6},

Increasing

: \frac{- 1429 + 71}{6} < x < \frac{1429 + 71}{6},

Decreasing

: \frac{1429 + 71}{6} < x < \infty

Plug

x = \frac{71 - 1429}{6}

into

x (15 - 43 + 2 x) (\frac{43}{2} - x) : - \frac{26767 + 1429 1429}{54}

Minimum (\frac{71 - 1429}{6}, - \frac{26767 + 1429 1429}{54})

Plug

x = \frac{71 + 1429}{6}

into

x (15 - 43 + 2 x) (\frac{43}{2} - x) : \frac{1429 1429 - 26767}{54}

Maximum (\frac{71 + 1429}{6}, \frac{1429 1429 - 26767}{54})

Minimum (\frac{71 - 1429}{6}, - \frac{26767 + 1429 1429}{54}), Maximum (\frac{71 + 1429}{6}, \frac{1429 1429 - 26767}{54})

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Frequently Asked Questions (FAQ)

What is the extreme f(x)=x(15-43+2x)(43/2-x) ?
The extreme f(x)=x(15-43+2x)(43/2-x) is