Earp, you did nothing wrong that day - perhaps outing your fos would have helped, but it was up to me and Lawls to catch Banana, and we failed to make it happen. The loss is on us.
On using a secant to differentiate: suppose f(x) is differentiable on the interval [C, C+deltaC]. Graph the function and draw a secant line through the points (C, f(C)) and (C+deltaC, f(C+deltaC)). Consider the slope of this line and take the limit as deltaC approaches zero. Look familiar?