Is \(\displaystyle{f{{\left({x}\right)}}}=-{9}{x}^{{{5}}}+{15}{x}^{{{4}}}-{21}{x}^{{{2}}}-{8}{x}+{2}\) concave or convex at

Brooks Barker

Brooks Barker

Answered question

2022-04-13

Is f(x)=9x5+15x421x28x+2 concave or convex at x=3?

Answer & Explanation

muthe2ulj

muthe2ulj

Beginner2022-04-14Added 10 answers

Step 1
Concavity/convexity must be tested, therefore evaluate f (x)
If f (x)>0 then is convex
If f (x) then f(x) is concaveNKSrequire to find f (x) and then value of f (3)
f(x)=45x4+60x342x8
f (x)=180x3+180x242
f (3)=180(3)3+180(3)242
=4860+162042=3282<0
Since f (3)<0 then f(x) is concave at x=3

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