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Popular Calculus >

f(x)= x/(4x+3ln(x))

Solution

f (x) = \frac{x}{4 x + 3 ln ( x )}

Solution

Domain : 0 < x < \frac{3 W _{0} ( \frac{4}{3} )}{4} or x > \frac{3 W _{0} ( \frac{4}{3} )}{4}

Range : f (x) < 0 or f (x) \geq \frac{e}{4 e + 3}

Intercepts : None

Asymptotes : Vertical x = \frac{3 W _{0} ( \frac{4}{3} )}{4}, Horizontal y = \frac{1}{4}

Extreme Points : Minimum (e, \frac{e}{4 e + 3})

+1

Interval Notation

Domain : (0, \frac{3 W _{0} ( \frac{4}{3} )}{4}) \cup (\frac{3 W _{0} ( \frac{4}{3} )}{4}, \infty)

Range : (- \infty, 0) \cup [\frac{e}{4 e + 3}, \infty)

Solution steps

Domain of

\frac{x}{4 x + 3 ln ( x )} : 0 < x < \frac{3 W _{0} ( \frac{4}{3} )}{4} or x > \frac{3 W _{0} ( \frac{4}{3} )}{4}

Range of

\frac{x}{4 x + 3 ln ( x )} : f (x) < 0 or f (x) \geq \frac{e}{4 e + 3}

Axis interception points of

\frac{x}{4 x + 3 ln ( x )} :

None

Asymptotes of

\frac{x}{4 x + 3 ln ( x )} :

Vertical

: x = \frac{3 W _{0} ( \frac{4}{3} )}{4},

Horizontal

: y = \frac{1}{4}

Extreme Points of

\frac{x}{4 x + 3 ln ( x )} :

Minimum

(e, \frac{e}{4 e + 3})

Graph

Popular Examples

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s l o p e y = \frac{- 4 x ^{2} + 12}{2 x + 2}

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limit as x approaches-9 of 1-4x^3

x \to - 9 lim (1 - 4 x^{3})

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\int_{0}^{5} 2 e^{x} d x

limit as x approaches 2 of 3x^3+5x

x \to 2 lim (3 x^{3} + 5 x)

Frequently Asked Questions (FAQ)

What is the f(x)= x/(4x+3ln(x)) ?
The f(x)= x/(4x+3ln(x)) is