# When gradient of utility function is a zero vector

In Advanced Microeconomic theory by Jehle and Reny is said that if $\mathbf{x^*}$ is a solution to the following maximization problem $\max_{\mathbf{x} \in \mathbb{R}_+^n} u(\mathbf{x})$ subject to $\mathbf{p \cdot x}\le y$, then $\bigtriangledown u(\mathbf{x^*})=\mathbf{0}$
is possible but quite unlikely.

The question is why is it quite unlikely? I can think only budget constraint, but is it right?

$$u(x) =ax - bx^2$$