Is \(\displaystyle{f{{\left({x}\right)}}}={4}{x}^{{5}}-{x}^{{4}}-{9}{x}^{{3}}+{5}{x}^{{2}}-{7}{x}\) concave or convex at

Ormezzani6cuu

Ormezzani6cuu

Answered question

2022-04-16

Is f(x)=4x5x49x3+5x27x concave or convex at x=1?

Answer & Explanation

WigwrannyErarmbmk

WigwrannyErarmbmk

Beginner2022-04-17Added 13 answers

Step 1
To determine if a function is concave/convex we calculate the value of f''(x) at x=a.
- If fa)>0, then f(x) is convex at x=a
- If fa)<0, then f(x) is concave at x=a
f(x)=4x5x49x3+5x27x
Step 2
Differentiate using the power rule
f(x)=20x44x327x2+10x7
and f(x)=80x312x254x+10
so f1)=80(1)312(1)254(1)+10
=8012+54+10=28

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