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Popular Functions >

extreme f(x)=x(25-39+2x)(39/2-x)

Solution

extreme

Solution

Minimum (\frac{53 - 1171}{6}, \frac{18656 - 1171 1171}{54}), Maximum (\frac{53 + 1171}{6}, \frac{1171 1171 + 18656}{54})

Solution steps

f^{'} (x) = - 6 x^{2} + 106 x - 273

Find intervals:

Decreasing

: - \infty < x < \frac{- 1171 + 53}{6},

Increasing

: \frac{- 1171 + 53}{6} < x < \frac{1171 + 53}{6},

Decreasing

: \frac{1171 + 53}{6} < x < \infty

Plug

x = \frac{53 - 1171}{6}

into

x (25 - 39 + 2 x) (\frac{39}{2} - x) : \frac{18656 - 1171 1171}{54}

Minimum (\frac{53 - 1171}{6}, \frac{18656 - 1171 1171}{54})

Plug

x = \frac{53 + 1171}{6}

into

x (25 - 39 + 2 x) (\frac{39}{2} - x) : \frac{1171 1171 + 18656}{54}

Maximum (\frac{53 + 1171}{6}, \frac{1171 1171 + 18656}{54})

Minimum (\frac{53 - 1171}{6}, \frac{18656 - 1171 1171}{54}), Maximum (\frac{53 + 1171}{6}, \frac{1171 1171 + 18656}{54})

Graph

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Frequently Asked Questions (FAQ)

What is the extreme f(x)=x(25-39+2x)(39/2-x) ?
The extreme f(x)=x(25-39+2x)(39/2-x) is