Let f(x,y) = -(x³ - 3xy²/x). At the point (1,-3), in which direction is f increasing the fastest, and what is the rate of increase in that direction?

a) Direction: Along the x-axis; Rate: 6
b) Direction: Along the y-axis; Rate: 3
c) Direction: Diagonal; Rate: 0
d) Direction: Along the x-axis; Rate: -6