Consider the differential equation $\frac{dy}{dx}=ky(10-y).$ Let $y=f(x)$ be the particular solution to the differential equation with the initial condition $f(0)=1.$

Part A: Use Euler's method with two steps of equal size to approximate $f(2)$ in terms of $k.$

Part B: Find $f^{\text{'}\text{'}}(0)$ in terms of $k$ and $y.$