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Popular >

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

Solution

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

Solution

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

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

Intercepts : None

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

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

+1

Solution steps

Domain of

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

Range of

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

Axis interception points of

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

None

Asymptotes of

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

Vertical

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

Horizontal

: y = \frac{1}{3}

Extreme Points of

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

Minimum

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

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Frequently Asked Questions (FAQ)

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