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Popular Functions >

extreme f(x)=x(27-41+2x)(41/2-x)

Solution

extreme

Solution

Minimum (\frac{55 - 1303}{6}, \frac{24310 - 1303 1303}{54}), Maximum (\frac{55 + 1303}{6}, \frac{1303 1303 + 24310}{54})

Solution steps

f^{'} (x) = - 6 x^{2} + 110 x - 287

Find intervals:

Decreasing

: - \infty < x < \frac{- 1303 + 55}{6},

Increasing

: \frac{- 1303 + 55}{6} < x < \frac{1303 + 55}{6},

Decreasing

: \frac{1303 + 55}{6} < x < \infty

Plug

x = \frac{55 - 1303}{6}

into

x (27 - 41 + 2 x) (\frac{41}{2} - x) : \frac{24310 - 1303 1303}{54}

Minimum (\frac{55 - 1303}{6}, \frac{24310 - 1303 1303}{54})

Plug

x = \frac{55 + 1303}{6}

into

x (27 - 41 + 2 x) (\frac{41}{2} - x) : \frac{1303 1303 + 24310}{54}

Maximum (\frac{55 + 1303}{6}, \frac{1303 1303 + 24310}{54})

Minimum (\frac{55 - 1303}{6}, \frac{24310 - 1303 1303}{54}), Maximum (\frac{55 + 1303}{6}, \frac{1303 1303 + 24310}{54})

Graph

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Frequently Asked Questions (FAQ)

What is the extreme f(x)=x(27-41+2x)(41/2-x) ?
The extreme f(x)=x(27-41+2x)(41/2-x) is