Is \(\displaystyle{f{{\left({x}\right)}}}={x}^{{{5}}}-{4}{x}^{{{4}}}+{16}{x}-{4}\) concave or convex at

Brooks Barker

Brooks Barker

Answered question

2022-04-16

Is f(x)=x54x4+16x4 concave or convex at x=2?

Answer & Explanation

gsmckibbenx7ga

gsmckibbenx7ga

Beginner2022-04-17Added 17 answers

Step 1
Let's calculate the first and second derivatives
f(x)=x54x4+16x4
f(x)=5x416x3+16
f(x)=20x348x2=4x2(5x12)
Now, we calculate, f(2)
f(2)=20(2)348(2)2
=160192=352
As, f(2)<0, we conclude that f(2) is concave
Normally, we calculate the concavity over an interval for example
], 0[

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