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Popular >

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

Solution

extreme points

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

Solution

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

Solution steps

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

Find intervals:

Increasing

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

Decreasing

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

Increasing

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

Plug

x = - \frac{2}{3}

into

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

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

Plug

x = \frac{2}{3}

into

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

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

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

Popular Examples

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domain of f(x)= 1/(x-9)domain

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parity f(x)=(5xtan(x))/(x^2+1)parity

f (x) = \frac{5 x tan ( x )}{x ^{2} + 1}

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f (x) = \frac{5 - 2 x}{6 x + 3}

Frequently Asked Questions (FAQ)

What is the extreme f(x)=x^3-2x ?
The extreme f(x)=x^3-2x is