What is the f(x)=2xln(x)+x ?

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f(x)=2xln(x)+x

f (x) = 2 x ln (x) + x

Domain : x > 0

Range : f (x) \geq - \frac{2}{e ^{\frac{3}{2}}}

X Intercepts : (\frac{1}{e}, 0)

Asymptotes : None

Extreme Points : Minimum (\frac{1}{e ^{\frac{3}{2}}}, - \frac{2}{e ^{\frac{3}{2}}})

Interval Notation

Domain : (0, \infty)

Range : [- \frac{2}{e ^{\frac{3}{2}}}, \infty)

Solution steps

Domain of

2 x ln (x) + x : x > 0

Range of

2 x ln (x) + x : f (x) \geq - \frac{2}{e ^{\frac{3}{2}}}

Axis interception points of

2 x ln (x) + x :

X Intercepts

: (\frac{1}{e}, 0)

Asymptotes of

2 x ln (x) + x :

None

Extreme Points of

2 x ln (x) + x :

Minimum

(\frac{1}{e ^{\frac{3}{2}}}, - \frac{2}{e ^{\frac{3}{2}}})

\int (\frac{5 - 10 x ^{2}}{4 x ^{3} - 6 x + 15}) d x

f (x) = x x^{2} + 21

x \to \infty lim (1 + 4 x)

x^{2} \frac{d y}{d x} - x y + 1 = 0

x \to \infty lim (- \frac{x}{x})