Is \(\displaystyle{f{{\left({x}\right)}}}=-{x}{e}^{{{x}}}+{x}^{{{3}}}-{x}^{{{2}}}\) concave or convex at

painter555ui8n

painter555ui8n

Answered question

2022-04-16

Is f(x)=xex+x3x2 concave or convex at x=2?

Answer & Explanation

WigwrannyErarmbmk

WigwrannyErarmbmk

Beginner2022-04-17Added 13 answers

Step 1
First, you would calculate the first and the second derivatives:
f(x)=(1ex+(x)ex)+3x22x
=(exxex)+3x22x
fx)=(exexxex)+6x2
=2exxex+6x2
Step 2
Then you would calculate
f2)=2e2(2)e2+6(2)2
=-2e-2+2e-2-12-2
14<0
Since f2)<0, the function is concave

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