Let $f\left(x\right)$  be a function defined as follows: $f\left(x\right)=\sin (x^2-3x),x\le 0$ ; and at $6x+5x^2,x>0$  then at $x=0$ $, f\left(x\right)$

$f\left(0\right)=\sin 0=0\Rightarrow f\left(0^{+}\right)\to 0^{+}$

$\Rightarrow f\left(0^{-}\right)=\underset{x\to 0^{-}}{lim}\sin (x^2-3x)=\underset{h\to 0}{lim}\sin (h^2+3h)\to 0^{+}$

Thus, $f\left(0^{+}\right)>f\left(0\right)$ and  $f\left(0^{-}\right)>f\left(0\right)$. 

Hence, $x=0$  is a point of minima.