Is $f (x) = \frac{{(x - 9)}^{3}}{\frac{x^{2}}{3} + 1}$ $f(x) =(x-9)^3/(x^2/3+1)$ concave or convex at $x = 9$ $x=9$ ?

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Answer 1 · 2017-09-29T11:55:03

Neither.

At x=9, The function is zero, its first derivative is zero, its second derivative is zero, and so on.

So the function is neither concave nor convex at x = 9.

Is f(x)=(x−9)3x23+1f(x) =(x-9)^3/(x^2/3+1) concave or convex at x=9x=9?