\(\displaystyle{f{{\left({x}\right)}}}={4}{x}^{{{5}}}+{2}{x}^{{{3}}}-{2}{x}^{{{2}}}+{2}{x}+{8}\) concave or convex at \(\displaystyle{x}=-{3}\)?

Samara Richard

Samara Richard

Answered question

2022-03-31

f(x)=4x5+2x32x2+2x+8 concave or convex at x=3?

Answer & Explanation

Harry Gibson

Harry Gibson

Beginner2022-04-01Added 13 answers

Step 1
To determine if a function is concave/convex at f(a) we require to find the value of f(a).
If f(a)>0, then f(x) is convex at x=a
If f(a)<0, then f(x) is concave at x=a
hence f(x)=4x5+2x32x2+2x+8
f(x)=20x4+6x24x+2
and f(x)=80x3+12x4
f(3)=80(3)3+12(3)4=2200
Since f(3)<0, then f(x) is concave at x=3

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