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Popular >

extreme 1/(x^3-2x)

Solution

extreme points

\frac{1}{x ^{3} - 2 x}

Solution

Minimum - \frac{2}{3}, \frac{27 ( ( \frac{2}{3} ) ^{\frac{3}{2}} + 2 \frac{2}{3} )}{64}, Maximum \frac{2}{3}, - \frac{27 ( ( \frac{2}{3} ) ^{\frac{3}{2}} + 2 \frac{2}{3} )}{64}

Solution steps

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

Find intervals:

Decreasing

: - \infty < x < - 2,

Decreasing

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

Increasing

: - \frac{2}{3} < x < 0,

Increasing

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

Decreasing

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

Decreasing

: 2 < x < \infty

Plug

x = - \frac{2}{3}

into

\frac{1}{x ^{3} - 2 x} : \frac{27 ( ( \frac{2}{3} ) ^{\frac{3}{2}} + 2 \frac{2}{3} )}{64}

Minimum - \frac{2}{3}, \frac{27 ( ( \frac{2}{3} ) ^{\frac{3}{2}} + 2 \frac{2}{3} )}{64}

Plug

x = \frac{2}{3}

into

\frac{1}{x ^{3} - 2 x} : - \frac{27 ( ( \frac{2}{3} ) ^{\frac{3}{2}} + 2 \frac{2}{3} )}{64}

Maximum \frac{2}{3}, - \frac{27 ( ( \frac{2}{3} ) ^{\frac{3}{2}} + 2 \frac{2}{3} )}{64}

Minimum - \frac{2}{3}, \frac{27 ( ( \frac{2}{3} ) ^{\frac{3}{2}} + 2 \frac{2}{3} )}{64}, Maximum \frac{2}{3}, - \frac{27 ( ( \frac{2}{3} ) ^{\frac{3}{2}} + 2 \frac{2}{3} )}{64}

Popular Examples

extreme f(x,y)=4y^3x^2-12y^2-36y+2 extreme points

f (x, y) = 4 y^{3} x^{2} - 12 y^{2} - 36 y + 2

extreme f(x)=4x^2+5x-2 extreme points

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

extreme f(x)=x^5+3x^4-2x+1 extreme points

f (x) = x^{5} + 3 x^{4} - 2 x + 1

extreme f(x)=-2x^3+39x^2-240,4<= x<= 9 extreme points

f (x) = - 2 x^{3} + 39 x^{2} - 240, 4 \leq x \leq 9

extreme f(x)=3x^2e^{-2x}+1 extreme points

f (x) = 3 x^{2} e^{- 2 x} + 1

Frequently Asked Questions (FAQ)

What is the extreme 1/(x^3-2x) ?
The extreme 1/(x^3-2x) is