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Popular >

extreme f(x)=(x^2)/((x-4)^2)

Solution

extreme points

f (x) = \frac{x ^{2}}{( x - 4 ) ^{2}}

Solution

Minimum (0, 0)

Solution steps

f^{'} (x) = - \frac{8 x}{( x - 4 ) ^{3}}

Find intervals:

Decreasing

: - \infty < x < 0,

Increasing

: 0 < x < 4,

Decreasing

: 4 < x < \infty

Plug

x = 0

into

\frac{x ^{2}}{( x - 4 ) ^{2}} : 0

Minimum (0, 0)

Popular Examples

extreme f(x,y)=4x^2+4y^2+x^4+y^4-6x^2y^2 extreme points

f (x, y) = 4 x^{2} + 4 y^{2} + x^{4} + y^{4} - 6 x^{2} y^{2}

extreme f(x,y)=16xy-x^3-8y^2 extreme points

f (x, y) = 16 x y - x^{3} - 8 y^{2}

extreme f(x,y)=x^3+3/2 y^2-3xy-124 extreme points

f (x, y) = x^{3} + \frac{3}{2} y^{2} - 3 x y - 124

extreme 3x^4-4x^3+1 extreme points

3 x^{4} - 4 x^{3} + 1

extreme f(x,y)=8x^4+y^2-16xy extreme points

f (x, y) = 8 x^{4} + y^{2} - 16 x y

Frequently Asked Questions (FAQ)

What is the extreme f(x)=(x^2)/((x-4)^2) ?
The extreme f(x)=(x^2)/((x-4)^2) is Minimum(0,0)