Is \(\displaystyle{f{{\left({x}\right)}}}={x}^{{{3}}}-{2}{x}+{7}\) concave or convex at

daurialebraslmc

daurialebraslmc

Answered question

2022-04-13

Is f(x)=x32x+7 concave or convex at x=2?

Answer & Explanation

annieljcddj0

annieljcddj0

Beginner2022-04-14Added 15 answers

Step 1
To determine if a function f(x) is concave/convex at x = 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
Step 2
Now f(x)=x32x+7
differentiate using the power rule
f(x)=3x22
and fx)=6x
f2)=(6×2)=12
Since f2)>0 then f(x) is convex at x=2.

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