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

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

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

Domain : x > 0

Range : 0 < f (x) \leq \frac{e}{4 e - 3}

Intercepts : None

Asymptotes : Horizontal y = \frac{1}{4}

Extreme Points : Maximum (e, \frac{e}{4 e - 3})

Interval Notation

Domain : (0, \infty)

Range : (0, \frac{e}{4 e - 3}]

Solution steps

Domain of

\frac{x}{4 x - 3 ln ( x )} : x > 0

Range of

\frac{x}{4 x - 3 ln ( x )} : 0 < f (x) \leq \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 )} :

Horizontal

: y = \frac{1}{4}

Extreme Points of

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

Maximum

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

\frac{d}{d x} (e^{(\frac{x}{2})^{2}})

\frac{d}{d x} (\frac{( 2 x ^{2} )}{x - 2})

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

\frac{d}{d x} (3 cos (x) - 4 sin (x))

\frac{e ^{x}}{7 x ^{2} + 5}