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Popular >

extreme x/(x^2+100)

Solution

extreme points

\frac{x}{x ^{2} + 100}

Solution

Minimum (- 10, - \frac{1}{20}), Maximum (10, \frac{1}{20})

Solution steps

f^{'} (x) = \frac{- x ^{2} + 100}{( x ^{2} + 100 ) ^{2}}

Find intervals:

Decreasing

: - \infty < x < - 10,

Increasing

: - 10 < x < 10,

Decreasing

: 10 < x < \infty

Plug

x = - 10

into

\frac{x}{x ^{2} + 100} : - \frac{1}{20}

Minimum (- 10, - \frac{1}{20})

Plug

x = 10

into

\frac{x}{x ^{2} + 100} : \frac{1}{20}

Maximum (10, \frac{1}{20})

Minimum (- 10, - \frac{1}{20}), Maximum (10, \frac{1}{20})

Popular Examples

extreme f(x)=(4860)/x+15x+717904 extreme points

f (x) = \frac{4860}{x} + 15 x + 717904

extreme f(x,y)=-x^3+4xy-2y^2+4x+1 extreme points

f (x, y) = - x^{3} + 4 x y - 2 y^{2} + 4 x + 1

extreme f(x,y)=x^3+y^3+9x^2-3y^2+15x-9y extreme points

f (x, y) = x^{3} + y^{3} + 9 x^{2} - 3 y^{2} + 15 x - 9 y

extreme f(x)=2x+sin(4x)extreme points

f (x) = 2 x + sin (4 x)

extreme y=(x^2-7)/(x-4)extreme points

y = \frac{x ^{2} - 7}{x - 4}

Frequently Asked Questions (FAQ)

What is the extreme x/(x^2+100) ?
The extreme x/(x^2+100) is Minimum(-10,-1/20),Maximum(10, 1/20)