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Popular >

extreme (x^3)/(x-2)

Solution

extreme points

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

Solution

Saddle (0, 0), Minimum (3, 27)

Solution steps

f^{'} (x) = \frac{2 x ^{3} - 6 x ^{2}}{( x - 2 ) ^{2}}

Find intervals:

Decreasing

: - \infty < x < 0,

Decreasing

: 0 < x < 2,

Decreasing

: 2 < x < 3,

Increasing

: 3 < x < \infty

Plug

x = 0

into

\frac{x ^{3}}{x - 2} : 0

Saddle (0, 0)

Plug

x = 3

into

\frac{x ^{3}}{x - 2} : 27

Minimum (3, 27)

Saddle (0, 0), Minimum (3, 27)

Popular Examples

extreme f(x)=sqrt(-x^2+4),-1<= x<= 2 extreme points

f (x) = - x^{2} + 4, - 1 \leq x \leq 2

extreme f(x)=20x^3+9x^2-24x+12,0<= x<= 1 extreme points

f (x) = 20 x^{3} + 9 x^{2} - 24 x + 12, 0 \leq x \leq 1

extreme 5x^3-30x^2+45x extreme points

5 x^{3} - 30 x^{2} + 45 x

extreme f(x)=-x+2cos(x),0<= x<= 2pi extreme points

f (x) = - x + 2 cos (x), 0 \leq x \leq 2 π

extreme+sqrt((x-1)^2)extreme points

+ (x - 1)^{2}

Frequently Asked Questions (FAQ)

What is the extreme (x^3)/(x-2) ?
The extreme (x^3)/(x-2) is Saddle(0,0),Minimum(3,27)