Is #f(x)=-x^5-21x^4-2x^3+4x-30# concave or convex at #x=0#?

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Is #f(x)=-x^5-21x^4-2x^3+4x-30# concave or convex at #x=0#?

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Answer 1 · 2016-05-23T12:28:42

inflexion point

Explanation:

Calculating the first derivative of #f(x)=-x^5-21x^4-2x^3+4x-30#
at #x=0# we get #f_x(0)=0# The second derivative gives
#f_{x x}(0) = 0# and the third #f_{x x x}(0)=-12# so the origin is an inflexion point. In this point the function behavior is like #-abs(c_0) x^3#. Nor concave or convex.

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Is #f(x)=-x^5-21x^4-2x^3+4x-30# concave or convex at #x=0#?

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