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Popular >

extreme f(x)= 2/3 x^3-4x^2-45x

Solution

extreme points

f (x) = \frac{2}{3} x^{3} - 4 x^{2} - 45 x

Solution

Maximum (\frac{4 - 106}{2}, - 2 (61 - 4106) + \frac{64 + 29 106}{3}), Minimum (\frac{4 + 106}{2}, - 2 (61 + 4106) + \frac{64 - 29 106}{3})

Solution steps

f^{'} (x) = 2 x^{2} - 8 x - 45

Find intervals:

Increasing

: - \infty < x < - \frac{53}{2} + 2,

Decreasing

: - \frac{53}{2} + 2 < x < \frac{53}{2} + 2,

Increasing

: \frac{53}{2} + 2 < x < \infty

Plug

x = \frac{4 - 106}{2}

into

\frac{2}{3} x^{3} - 4 x^{2} - 45 x : - 2 (61 - 4106) + \frac{64 + 29 106}{3}

Maximum (\frac{4 - 106}{2}, - 2 (61 - 4106) + \frac{64 + 29 106}{3})

Plug

x = \frac{4 + 106}{2}

into

\frac{2}{3} x^{3} - 4 x^{2} - 45 x : - 2 (61 + 4106) + \frac{64 - 29 106}{3}

Minimum (\frac{4 + 106}{2}, - 2 (61 + 4106) + \frac{64 - 29 106}{3})

Maximum (\frac{4 - 106}{2}, - 2 (61 - 4106) + \frac{64 + 29 106}{3}), Minimum (\frac{4 + 106}{2}, - 2 (61 + 4106) + \frac{64 - 29 106}{3})

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Frequently Asked Questions (FAQ)

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