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Popular >

extreme f(x)=(x^2(x-1))/(x+2)

Solution

extreme points

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

Solution

Minimum (\frac{- 5 - 57}{4}, \frac{19 57 + 143}{8}), Maximum (0, 0), Minimum (\frac{- 5 + 57}{4}, - \frac{19 57 - 143}{8})

Solution steps

f^{'} (x) = \frac{2 x ^{3} + 5 x ^{2} - 4 x}{( x + 2 ) ^{2}}

Find intervals:

Decreasing

: - \infty < x < \frac{- 5 - 57}{4},

Increasing

: \frac{- 5 - 57}{4} < x < - 2,

Increasing

: - 2 < x < 0,

Decreasing

: 0 < x < \frac{57 - 5}{4},

Increasing

: \frac{57 - 5}{4} < x < \infty

Plug

x = \frac{- 5 - 57}{4}

into

\frac{x ^{2} ( x - 1 )}{x + 2} : \frac{19 57 + 143}{8}

Minimum (\frac{- 5 - 57}{4}, \frac{19 57 + 143}{8})

Plug

x = 0

into

\frac{x ^{2} ( x - 1 )}{x + 2} : 0

Maximum (0, 0)

Plug

x = \frac{- 5 + 57}{4}

into

\frac{x ^{2} ( x - 1 )}{x + 2} : - \frac{19 57 - 143}{8}

Minimum (\frac{- 5 + 57}{4}, - \frac{19 57 - 143}{8})

Minimum (\frac{- 5 - 57}{4}, \frac{19 57 + 143}{8}), Maximum (0, 0), Minimum (\frac{- 5 + 57}{4}, - \frac{19 57 - 143}{8})

Popular Examples

extreme f(x)=2x^3-3x^2-36x+1 extreme points

f (x) = 2 x^{3} - 3 x^{2} - 36 x + 1

extreme f(x,y)=2x^2+4xy^3-2y^2+15 extreme points

f (x, y) = 2 x^{2} + 4 x y^{3} - 2 y^{2} + 15

extreme f(x)=2x^3-3x^2-12x-7 extreme points

f (x) = 2 x^{3} - 3 x^{2} - 12 x - 7

extreme f(x,y)=x^2+y^2+xy-2x-y+1 extreme points

f (x, y) = x^{2} + y^{2} + x y - 2 x - y + 1

extreme f(x)=xsqrt(x^2+16)extreme points

f (x) = x x^{2} + 16

Frequently Asked Questions (FAQ)

What is the extreme f(x)=(x^2(x-1))/(x+2) ?
The extreme f(x)=(x^2(x-1))/(x+2) is