$\backslash$table$[[y,8,9,10,11,12],[g(y),-7,2,4,-3,-9]]$

Let $y=f(x)$ be the solution to the differential equation $\frac{dy}{dz}=4xg(y)$ with the initial condition $f(1)=10.$ Selected values of $g$ are given in the table above. What is the approximation for $f(1\mathrm{.}5)$ obtained by using Fider's method with a atep size of $0\mathrm{.}25$ starting at $x=1?$

$8\mathrm{.}5$

$11$

$11\mathrm{.}75$

$($D$)12$