Q: Find the local extrema of f(x)=x\log \left(x\right)

\begin{align}&\textrm{The local minimum is }-\frac{\log_{10}{\left(e\right)}}{e}\textrm{ at }x = \frac{1}{e}\end{align}

Q: Find the increasing or decreasing interval of f(x)=x\log \left(x\right)

\begin{align}&\textrm{The increasing interval is}\textrm{ }x\geq \frac{1}{e}\\&\textrm{The decreasing interval is}\textrm{ }0

Q: Find the vertical asymptotes of f(x)=x\log \left(x\right)

\textrm{No vertical asymptotes}

Q: Find the horizontal asymptotes of f(x)=x\log \left(x\right)

\textrm{No horizontal asymptotes}

Q: Testing for symmetry about the origin of f(x)=x\log \left(x\right)

\textrm{Not symmetry with respect to the origin}

Q: Testing for symmetry about the x-axis of f(x)=x\log \left(x\right)

\textrm{Not symmetry with respect to the x-axis}

Q: Testing for symmetry about the y-axis of f(x)=x\log \left(x\right)

\textrm{Not symmetry with respect to the y-axis}

Question 1

Evaluate the derivative of f(x)=x\log \left(x\right)

Accepted Answer

f^{\prime}\left(x\right)=\frac{\ln{\left(x\right)}+1}{\ln{\left(10\right)}}

Question 2

Find the domain of f(x)=x\log \left(x\right)

Accepted Answer

Question 3

ext{Find the }x	ext{-intercept/zero} of f(x)=x\log \left(xight)

Accepted Answer

Question 4

Find the y-intercept of f(x)=x\log \left(x\right)

Accepted Answer

extrm{No y-intercept}

Question 5

Find the critical numbers of f(x)=x\log \left(x\right)

Accepted Answer

x=\frac{1}{e}

Question 6

Find the local extrema of f(x)=x\log \left(x\right)

Accepted Answer

\begin{align}& extrm{The local minimum is }-\frac{\log_{10}{\left(e ight)}}{e} extrm{ at }x = \frac{1}{e}\end{align}

Question 7

Find the increasing or decreasing interval of f(x)=x\log \left(x\right)

Accepted Answer

\begin{align}& extrm{The increasing interval is} extrm{ }x\geq \frac{1}{e}\& extrm{The decreasing interval is} extrm{ }0

Question 8

Find the range of f(x)=x\log \left(x\right)

Accepted Answer

f\left(x\right)\geq -\frac{\log_{10}{\left(e\right)}}{e}

Question 9

Find the vertical asymptotes of f(x)=x\log \left(x\right)

Accepted Answer

extrm{No vertical asymptotes}

Question 10

Find the horizontal asymptotes of f(x)=x\log \left(x\right)

Accepted Answer

extrm{No horizontal asymptotes}

Question 11

Find the oblique asymptotes of f(x)=x\log \left(x\right)

Accepted Answer

extrm{No oblique asymptotes}

Question 12

Determine if even, odd or neither of f(x)=x\log \left(x\right)

Accepted Answer

extrm{Neither even nor odd}

Question 13

Find the stationary points of f(x)=x\log \left(x\right)

Accepted Answer

\left(\frac{1}{e},-\frac{\log_{10}{\left(e\right)}}{e}\right)

Question 14

Find the inflection points of f(x)=x\log \left(x\right)

Accepted Answer

extrm{No inflection points}

Question 15

Testing for symmetry about the origin of f(x)=x\log \left(x\right)

Accepted Answer

extrm{Not symmetry with respect to the origin}

Question 16

Testing for symmetry about the x-axis of f(x)=x\log \left(x\right)

Accepted Answer

extrm{Not symmetry with respect to the x-axis}

Question 17

Testing for symmetry about the y-axis of f(x)=x\log \left(x\right)

Accepted Answer

extrm{Not symmetry with respect to the y-axis}

f(x)=xlog (x)

Function

Testing for symmetry

Graph

Frequently Asked Questions

Evaluate the derivative of \(f(x)=x\log \left(x\right)\)

Find the domain of \(f(x)=x\log \left(x\right)\)

$Find the x -intercept/zero$ of \(f(x)=x\log \left(x\right)\)

Find the y-intercept of \(f(x)=x\log \left(x\right)\)

Find the critical numbers of \(f(x)=x\log \left(x\right)\)

Find the local extrema of \(f(x)=x\log \left(x\right)\)

Find the increasing or decreasing interval of \(f(x)=x\log \left(x\right)\)

Find the range of \(f(x)=x\log \left(x\right)\)

Find the vertical asymptotes of \(f(x)=x\log \left(x\right)\)

Find the horizontal asymptotes of \(f(x)=x\log \left(x\right)\)

Find the oblique asymptotes of \(f(x)=x\log \left(x\right)\)

Determine if even, odd or neither of \(f(x)=x\log \left(x\right)\)

Find the stationary points of \(f(x)=x\log \left(x\right)\)

Find the inflection points of \(f(x)=x\log \left(x\right)\)

Testing for symmetry about the origin of \(f(x)=x\log \left(x\right)\)

Testing for symmetry about the x-axis of \(f(x)=x\log \left(x\right)\)

Testing for symmetry about the y-axis of \(f(x)=x\log \left(x\right)\)