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Popular >

extreme y=x^3-2x

Solution

extreme points

y = 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

critical 1/(x^2-4)critical points

\frac{1}{x ^{2} - 4}

domain of f(x)=5x+4 domain

f (x) = 5 x + 4

domain of f(x)= 1/(cos(x-pi/3))domain

f (x) = \frac{1}{cos ( x - \frac{π}{3} )}

f (x) = 2 x + 1

domain of (x-5)^2-9 domain

(x - 5)^{2} - 9

Frequently Asked Questions (FAQ)

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