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Popular >

extreme x/(x^2+4)

Solution

extreme points

\frac{x}{x ^{2} + 4}

Solution

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

Solution steps

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

Find intervals:

Decreasing

: - \infty < x < - 2,

Increasing

: - 2 < x < 2,

Decreasing

: 2 < x < \infty

Plug

x = - 2

into

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

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

Plug

x = 2

into

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

Maximum (2, \frac{1}{4})

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

Popular Examples

inverse of g(x)=8e^{x^2+1}inverse

g (x) = 8 e^{x^{2} + 1}

extreme f(x)=x^3-12x^2-27x+9 extreme points

f (x) = x^{3} - 12 x^{2} - 27 x + 9

inflection f(x)=-x^4-4x^3+8x-1 inflection points

f (x) = - x^{4} - 4 x^{3} + 8 x - 1

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

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

inverse of f(x)=(x-9)/4 inverse

f (x) = \frac{x - 9}{4}

Frequently Asked Questions (FAQ)

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