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

Vanessa Mccarty

Vanessa Mccarty

Answered question

2022-04-16

Is f(x)=x3x+exx2 concave or convex at x=1?

Answer & Explanation

Assorrymarf0cgr

Assorrymarf0cgr

Beginner2022-04-17Added 10 answers

Explanation:
The function will be convex if the second derivative is positive, and concave if it is negative.
Step 1
The first derivative is: 3x2+(2x+1)ex2+x1
The second derivative is: 6x+(2x1)2ex2+x2ex2+x
Step 2
At x=1:
6+2e2=20.78 positive value

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