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Popular Functions >

extreme f(x)=x(16-39+2x)(39/2-x)

Solution

extreme

Solution

Minimum (\frac{62 - 1153}{6}, - \frac{11935 + 1153 1153}{54}), Maximum (\frac{62 + 1153}{6}, \frac{1153 1153 - 11935}{54})

Solution steps

f^{'} (x) = - 6 x^{2} + 124 x - \frac{897}{2}

Find intervals:

Decreasing

: - \infty < x < - \frac{1153}{6} + \frac{31}{3},

Increasing

: - \frac{1153}{6} + \frac{31}{3} < x < \frac{1153}{6} + \frac{31}{3},

Decreasing

: \frac{1153}{6} + \frac{31}{3} < x < \infty

Plug

x = \frac{62 - 1153}{6}

into

x (16 - 39 + 2 x) (\frac{39}{2} - x) : - \frac{11935 + 1153 1153}{54}

Minimum (\frac{62 - 1153}{6}, - \frac{11935 + 1153 1153}{54})

Plug

x = \frac{62 + 1153}{6}

into

x (16 - 39 + 2 x) (\frac{39}{2} - x) : \frac{1153 1153 - 11935}{54}

Maximum (\frac{62 + 1153}{6}, \frac{1153 1153 - 11935}{54})

Minimum (\frac{62 - 1153}{6}, - \frac{11935 + 1153 1153}{54}), Maximum (\frac{62 + 1153}{6}, \frac{1153 1153 - 11935}{54})

Graph

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Frequently Asked Questions (FAQ)

What is the extreme f(x)=x(16-39+2x)(39/2-x) ?
The extreme f(x)=x(16-39+2x)(39/2-x) is