For what values of x is f(x)=2x4+4x3+2x2−2 concave or convex?

talpajocotefnf3

talpajocotefnf3

Answered

2022-03-27

For what values of x is f(x)=2x4+4x3+2x22 concave or convex?

Answer & Explanation

yaum3xg1

yaum3xg1

Expert

2022-03-28Added 12 answers

Step 1
Given function:
f(x)=2x4+4x3+2x22
f(x)=8x3+12x2+4x
f(x)=24x2+24x+4
The function will be concave when f(x)0
24x2+24x+4
6x2+6x+10
(x+3+36)(x+336)0
x(336, 3+36)
Hence, the given function is concave in (336, 3+36)
the given function is convex in (, 336)(3+36, )

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