What is the range of x^2log_{e}(x) ?

The range of x^2log_{e}(x) is f(x)>=-1/(2e)

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range of x^2log_{e}(x)

range

x^{2} lo g_{e} (x)

f (x) \geq - \frac{1}{2 e}

Interval Notation

[- \frac{1}{2 e}, \infty)

Solution steps

Find the minimum and maximum value in each defined interval and unite the results

Domain of

x^{2} lo g_{e} (x) : x > 0

Simplify

x^{2} lo g_{e} (x) : x^{2} ln (x)

Extreme Points of

x^{2} ln (x) :

Minimum

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

Find the range for the interval

0 < x < \infty : - \frac{1}{2 e} \leq f (x) < \infty

Combine the ranges of all domain intervals to obtain the function range

f (x) \geq - \frac{1}{2 e}

2 cos (4 x + \frac{π}{2})

y = - 4

\frac{1}{1 - x ^{2}}

f (x) = x - 3 x^{3}

y = \frac{4}{3} x

What is the range of x^2log_{e}(x) ?
The range of x^2log_{e}(x) is f(x)>=-1/(2e)