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Popular Functions >

extreme f(x)=4x-2x^3-5

Solution

extreme points

f (x) = 4 x - 2 x^{3} - 5

Solution

Minimum (- \frac{2}{3}, - 4 \frac{2}{3} + 2 (\frac{2}{3})^{\frac{3}{2}} - 5), Maximum (\frac{2}{3}, 4 \frac{2}{3} - 2 (\frac{2}{3})^{\frac{3}{2}} - 5)

Solution steps

f^{'} (x) = - 6 x^{2} + 4

Find intervals:

Decreasing

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

Increasing

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

Decreasing

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

Plug

x = - \frac{2}{3}

into

4 x - 2 x^{3} - 5 : - 4 \frac{2}{3} + 2 (\frac{2}{3})^{\frac{3}{2}} - 5

Minimum (- \frac{2}{3}, - 4 \frac{2}{3} + 2 (\frac{2}{3})^{\frac{3}{2}} - 5)

Plug

x = \frac{2}{3}

into

4 x - 2 x^{3} - 5 : 4 \frac{2}{3} - 2 (\frac{2}{3})^{\frac{3}{2}} - 5

Maximum (\frac{2}{3}, 4 \frac{2}{3} - 2 (\frac{2}{3})^{\frac{3}{2}} - 5)

Minimum (- \frac{2}{3}, - 4 \frac{2}{3} + 2 (\frac{2}{3})^{\frac{3}{2}} - 5), Maximum (\frac{2}{3}, 4 \frac{2}{3} - 2 (\frac{2}{3})^{\frac{3}{2}} - 5)

Graph

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Frequently Asked Questions (FAQ)

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