Question
$a>0$ ,$b>0$, $x_0\in \mathbb{R}$,$t_0\in \mathbb{R}$ . The set D is defined as $D=\{(t,x)\in \mathbb{R^2}:|t-t_0|\leq a , |x-x_0|\leq b \}$ . $a(t,x)$ is a continuous function on $D$ . verify whether the function $f(t,x)=(1+a(t,x))x^2$ is lipschitz or not with respect to $x$ on $D$.
My approach: I tried to take values of $a$ and $b$ and tried to find an example for not Lipschitz. But I am unable to make it in general.
Please help in finding a general example.