Is \(\displaystyle{f{{\left({x}\right)}}}={3}{x}^{{5}}-{x}^{{3}}+{8}{x}^{{2}}-{x}+{3}\) concave or convex at

Gretchen Barker

Gretchen Barker

Answered question

2022-04-15

Is f(x)=3x5x3+8x2x+3 concave or convex at x=4?

Answer & Explanation

star04iks7

star04iks7

Beginner2022-04-16Added 14 answers

Answer:
To find the concavity of a function f(x), you will need to determine the second derivative, and then evaluate at at the given point. If the result of fa)>0, the function is concave up; if the result is negative, it it concave down.
f(x)=3x5x3+8x2x+3
f(x)=15x43x2+16x=1
f(x)=60x36x+16
f(4)=60(4)36(4)+16=3,800<0
Thus, f(x) is concave down at x=4.

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