For what values of x is # f(x) = -sqrt(x^3-9x # concave or convex?

1 Answer
JMicheli
Jul 12, 2016

The function is concave on the interval #{-3, 0}#.

Explanation:

The answer is easily determined by viewing the graph:

graph{-sqrt(x^3 - 9x) [-4.8, 6.603, -4.618, 1.086]}

We already know that the answer is only real for the intervals #{-3,0}# and #{3, infty}#. Other values will result in an imaginary number, so they're out as far as finding concavity or convexity.

The interval #{3, infty}# does not change direction, so it can be neither concave nor convex. Thus the only possible answer is #{-3,0}#, which, as can be seen from the graph, is concave.

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