$($ pts$.)$ Find the absolute maximum value of $f(x,y)=x^2+x+2y^2$ on the disk $x^2+y^{2}1.$

$($a$)\frac{9}{4}$

$($b$)2$

$($c$)-\frac{1}{4}$

$($d$)\frac{11}{4}$

$($e$)\frac{3+\sqrt[\phantom{2}]{2}}{2}$