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Popular >

extreme f(x)=4x^3-36x^2+80x

Solution

extreme points

f (x) = 4 x^{3} - 36 x^{2} + 80 x

Solution

Maximum (\frac{9 - 21}{3}, - 24 (17 - 321) + \frac{3888 - 592 21}{9}), Minimum (\frac{9 + 21}{3}, - 24 (17 + 321) + \frac{3888 + 592 21}{9})

Solution steps

f^{'} (x) = 12 x^{2} - 72 x + 80

Find intervals:

Increasing

: - \infty < x < - \frac{7}{3} + 3,

Decreasing

: - \frac{7}{3} + 3 < x < \frac{7}{3} + 3,

Increasing

: \frac{7}{3} + 3 < x < \infty

Plug

x = \frac{9 - 21}{3}

into

4 x^{3} - 36 x^{2} + 80 x : - 24 (17 - 321) + \frac{3888 - 592 21}{9}

Maximum (\frac{9 - 21}{3}, - 24 (17 - 321) + \frac{3888 - 592 21}{9})

Plug

x = \frac{9 + 21}{3}

into

4 x^{3} - 36 x^{2} + 80 x : - 24 (17 + 321) + \frac{3888 + 592 21}{9}

Minimum (\frac{9 + 21}{3}, - 24 (17 + 321) + \frac{3888 + 592 21}{9})

Maximum (\frac{9 - 21}{3}, - 24 (17 - 321) + \frac{3888 - 592 21}{9}), Minimum (\frac{9 + 21}{3}, - 24 (17 + 321) + \frac{3888 + 592 21}{9})

Popular Examples

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Frequently Asked Questions (FAQ)

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