Is \(\displaystyle{f{{\left({x}\right)}}}={3}{x}^{{5}}-{x}^{{3}}+{8}{x}^{{2}}-{x}\) concave or convex at

Rosa Townsend

Rosa Townsend

Answered question

2022-04-16

Is f(x)=3x5x3+8x2x concave or convex at x=0?

Answer & Explanation

Emelia Leon

Emelia Leon

Beginner2022-04-17Added 18 answers

Step 1
f(x) is concave at x=a if fa)>0.
f(x) is convex at x=a if fa)>0.
Here, f(x)=3x5x3+8x2x,a=0. Knowing that, let's take the second derivative.
f(x)=15x43x2+16x1
fx)=20x36x+16
Step 2
Evaluate at 0:
f0)=20(03)6(0)+16=16>0
f(x) is concave at x=0.

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