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Popular >

extreme f(x)=x(17-2x)(50/2-x)

Solution

extreme points

f (x) = x (17 - 2 x) (\frac{50}{2} - x)

Solution

Maximum (\frac{67 - 1939}{6}, \frac{1939 1939 - 44488}{54}), Minimum (\frac{67 + 1939}{6}, - \frac{44488 + 1939 1939}{54})

Solution steps

f^{'} (x) = 6 x^{2} - 134 x + 425

Find intervals:

Increasing

: - \infty < x < \frac{- 1939 + 67}{6},

Decreasing

: \frac{- 1939 + 67}{6} < x < \frac{1939 + 67}{6},

Increasing

: \frac{1939 + 67}{6} < x < \infty

Plug

x = \frac{67 - 1939}{6}

into

x (17 - 2 x) (\frac{50}{2} - x) : \frac{1939 1939 - 44488}{54}

Maximum (\frac{67 - 1939}{6}, \frac{1939 1939 - 44488}{54})

Plug

x = \frac{67 + 1939}{6}

into

x (17 - 2 x) (\frac{50}{2} - x) : - \frac{44488 + 1939 1939}{54}

Minimum (\frac{67 + 1939}{6}, - \frac{44488 + 1939 1939}{54})

Maximum (\frac{67 - 1939}{6}, \frac{1939 1939 - 44488}{54}), Minimum (\frac{67 + 1939}{6}, - \frac{44488 + 1939 1939}{54})

Graph

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Frequently Asked Questions (FAQ)

What is the extreme f(x)=x(17-2x)(50/2-x) ?
The extreme f(x)=x(17-2x)(50/2-x) is