Is \(\displaystyle{f{{\left({x}\right)}}}={x}{\ln{{x}}}-{x}\) concave or convex at

fanairana7lu1

fanairana7lu1

Answered question

2022-04-14

Is f(x)=xlnxx concave or convex at x=1?

Answer & Explanation

Frain4i62

Frain4i62

Beginner2022-04-15Added 16 answers

Step 1
f(x) is concave upward (convex) at a point x0 if fx0)>0 and concave downward (concave) at a point x0 if fx0)<0.
We have
fx)=ddxf(x)
=ddx(ddxxln(x)x)
=ddxln(x)
=1x
Step 2
Then, at x=1:
f(1)=11=1>0
Thus f(x) is convex at x=1.

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