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Popular Functions >

extreme f(x)=-462x+64x^2-2x^3

Solution

extreme

Solution

Minimum (\frac{32 - 331}{3}, - 154 (32 - 331) + \frac{131072 - 5482 331}{27}), Maximum (\frac{32 + 331}{3}, - 154 (32 + 331) + \frac{131072 + 5482 331}{27})

Solution steps

f^{'} (x) = - 462 + 128 x - 6 x^{2}

Find intervals:

Decreasing

: - \infty < x < \frac{- 331 + 32}{3},

Increasing

: \frac{- 331 + 32}{3} < x < \frac{331 + 32}{3},

Decreasing

: \frac{331 + 32}{3} < x < \infty

Plug

x = \frac{32 - 331}{3}

into

- 462 x + 64 x^{2} - 2 x^{3} : - 154 (32 - 331) + \frac{131072 - 5482 331}{27}

Minimum (\frac{32 - 331}{3}, - 154 (32 - 331) + \frac{131072 - 5482 331}{27})

Plug

x = \frac{32 + 331}{3}

into

- 462 x + 64 x^{2} - 2 x^{3} : - 154 (32 + 331) + \frac{131072 + 5482 331}{27}

Maximum (\frac{32 + 331}{3}, - 154 (32 + 331) + \frac{131072 + 5482 331}{27})

Minimum (\frac{32 - 331}{3}, - 154 (32 - 331) + \frac{131072 - 5482 331}{27}), Maximum (\frac{32 + 331}{3}, - 154 (32 + 331) + \frac{131072 + 5482 331}{27})

Graph

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Frequently Asked Questions (FAQ)

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