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Popular >

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

Solution

extreme points

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

Solution

Minimum (- 2, - \frac{1}{4})

Solution steps

f^{'} (x) = - \frac{1}{x ^{2}} - \frac{2}{x ^{3}}

Find intervals:

Decreasing

: - \infty < x < - 2,

Increasing

: - 2 < x < 0,

Decreasing

: 0 < x < \infty

Plug

x = - 2

into

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

Minimum (- 2, - \frac{1}{4})

Popular Examples

extreme f(x)=x^3-5x^2+3x+13 extreme points

f (x) = x^{3} - 5 x^{2} + 3 x + 13

extreme f(x,y)=x+4y+2/(xy)extreme points

f (x, y) = x + 4 y + \frac{2}{x y}

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

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

extreme f(x)=x^3-3x+10 extreme points

f (x) = x^{3} - 3 x + 10

extreme f(x,y)=2y^3-3xy+x^2-1 extreme points

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

Frequently Asked Questions (FAQ)

What is the extreme f(x)= 1/x+1/(x^2) ?
The extreme f(x)= 1/x+1/(x^2) is Minimum(-2,-1/4)