1
$\begingroup$

I would like to know the concavity of this function, $f(x)=x^\frac{2}{3}-3$, using the second derivative test. For my attempt I got concave downward for the interval of $(-\infty,0)$, and $(0,\infty)$. I made that assupmtion by guessing that the second derivative, $f''(x)=-\frac{2}{9}\frac{1}{x^\frac{4}{3}}$, is always negative since $x^\frac{4}{3}$ is always positive.

$\endgroup$
1
  • 2
    $\begingroup$ Yes, you are right, the function is always concave down. $\endgroup$ Jan 1, 2017 at 20:58

1 Answer 1

2
$\begingroup$

Yes, everything I see is right. As a pointer, you should check the domain of the function as well, since it isn't necessarily the case that $\frac1{x^{4/3}}$ is defined for all real numbers.

$\endgroup$

You must log in to answer this question.

Not the answer you're looking for? Browse other questions tagged .