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

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

1 Answer

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Answer 1 · 2016-05-13T18:51:49

Convex

Explanation:

Considering locally convex a curve when it has second derivative negative valued, $\frac{d^{2} f (x)}{{d x}^{2}} ∣_{x = - 2} = - 0.129572$ $(d^2f(x))/(dx^2)|_(x=-2) = -0.129572$

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

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Explanation:

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Is f(x)=x/(1-x^3e^(x/3)f(x)=x1−x3ex3f(x)=x/(1-x^3e^(x/3) concave or convex at x=-2x=−2x=-2?

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Explanation:

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