What is the f(x)=x^2ln(2x) ?

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f(x)=x^2ln(2x)

f (x) = x^{2} ln (2 x)

Domain : x > 0

Range : f (x) \geq - \frac{1}{8 e}

X Intercepts : (\frac{1}{2}, 0)

Asymptotes : None

Extreme Points : Minimum (\frac{1}{2 e}, - \frac{1}{8 e})

Interval Notation

Domain : (0, \infty)

Range : [- \frac{1}{8 e}, \infty)

Solution steps

Domain of

x^{2} ln (2 x) : x > 0

Range of

x^{2} ln (2 x) : f (x) \geq - \frac{1}{8 e}

Axis interception points of

x^{2} ln (2 x) :

X Intercepts

: (\frac{1}{2}, 0)

Asymptotes of

x^{2} ln (2 x) :

None

Extreme Points of

x^{2} ln (2 x) :

Minimum

(\frac{1}{2 e}, - \frac{1}{8 e})

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