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Popular >

extreme 1/(x^2+1)

Solution

extreme points

\frac{1}{x ^{2} + 1}

Solution

Maximum (0, 1)

Solution steps

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

Find intervals:

Increasing

: - \infty < x < 0,

Decreasing

: 0 < x < \infty

Plug

x = 0

into

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

Maximum (0, 1)

Popular Examples

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

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

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

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

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

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

extreme f(x)= 5/3 x^3+18x^2-32x-30 extreme points

f (x) = \frac{5}{3} x^{3} + 18 x^{2} - 32 x - 30

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

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

Frequently Asked Questions (FAQ)

What is the extreme 1/(x^2+1) ?
The extreme 1/(x^2+1) is Maximum(0,1)