Question 37$ABCD$ is a square with side of unit length. Points $E$ and $F$ are taken respectively on sides $AB$ and $AD$ so that $AE=AF$ and the quadrilateral $CDFE$ has maximum area. In square units this maximum area is:$\dfrac12$$\dfrac9{16}$$\dfrac{19}{32}$$\dfrac58$$\dfrac23$