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Popular >

extreme f(x)=68x-x^3

Solution

extreme points

f (x) = 68 x - x^{3}

Solution

Minimum (- \frac{2 17}{3}, - \frac{272 17}{3 3}), Maximum (\frac{2 17}{3}, \frac{272 17}{3 3})

Solution steps

f^{'} (x) = 68 - 3 x^{2}

Find intervals:

Decreasing

: - \infty < x < - \frac{2 17}{3},

Increasing

: - \frac{2 17}{3} < x < \frac{2 17}{3},

Decreasing

: \frac{2 17}{3} < x < \infty

Plug

x = - \frac{2 17}{3}

into

68 x - x^{3} : - \frac{272 17}{3 3}

Minimum (- \frac{2 17}{3}, - \frac{272 17}{3 3})

Plug

x = \frac{2 17}{3}

into

68 x - x^{3} : \frac{272 17}{3 3}

Maximum (\frac{2 17}{3}, \frac{272 17}{3 3})

Minimum (- \frac{2 17}{3}, - \frac{272 17}{3 3}), Maximum (\frac{2 17}{3}, \frac{272 17}{3 3})

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Frequently Asked Questions (FAQ)

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