Finding an optimal x of x^2*log(x) using cvx

I’m having a problem with x^2*log(x). Can I get the function’s optimal value using the CVX optimization tool? Or is there something different? Also, if possible can you give a piece of information about the gradient descent method for finding the function’s optimal value using CVX?

As seen from the 2nd derivative, x^2*log(x) is concave for x <= .2231301601 and convex for x >= .2231301601. Therefore, it is neither convex nor concave, and can’t be used in CVX for minimization or maximization.