Show that the function $f:\mathbb{R}^2\rightarrow\mathbb{R}$ given by

$$f(x,y)=x^4+6x^2y^2 + y^4 -\frac{9}{4}x-\frac{7}{4}$$

achieves its minimal value, and determine all the points $(x, y)\in\mathbb{R}^2$ at which it is achieved.