The monthly payment for a home loan is given by a function $f(P,r,N)$ where $P$ is the principal (the initial size of the loan), $r$ the interest rate, and $N$ the length of the loan in months. Interest rates are expressed as a decimal: A % interest rate is denoted by $r=0.04$. If $P=500000, r=0.04$, and $N=204$(a 17-year loan), then the monthly payment is $f(500000,0.04,204)=1379$. Furthermore, with these values we have $$\frac{\partial{f}}{\partial{P}}=0.0058, \quad \frac{\partial{f}}{\partial{r}}=8595, \quad \frac{\partial{f}}{\partial{N}}=-1.5905$$ Estimate:

(a) The change in monthly payment per $3000$ increase in loan principal:
$\Delta f \approx$ dollars
(b) The change in monthly payment if the interest rate changes from $r=0.04$ to $r=0.045$:
$\Delta f \approx$ dollars
(c) The change in monthly payment if the length of the loan changes from $17$ to $20$ years:
$\Delta f \approx$ dollars