Is \(\displaystyle{f{{\left({x}\right)}}}=-{x}^{{5}}+{3}{x}^{{4}}-{9}{x}^{{3}}-{2}{x}^{{2}}-{6}{x}\) concave or convex at

gabolzm6d

gabolzm6d

Answered question

2022-04-14

Is f(x)=x5+3x49x32x26x concave or convex at x=8?

Answer & Explanation

carlosegundoacyg

carlosegundoacyg

Beginner2022-04-15Added 10 answers

Step 1
When looking for the concavity of a function, it's best to find the second derivative, f"(x), of the function f(x)
When fx)<0, the f(x) is concave
When fx)>0, the f(x) is convex
The first derivative of this function is:
f(x)=5x4+12x327x24x6
Step 2
The second derivative is:
f(x)=20x3+36x254x4
Plug in x=8 to get:
f(8)=20(8)3+36(8)254(8)4
f(8)=8372
Since f8)<0, the f(x) is concave at x=8.

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