Dear Cara. The first derivative with the given particular parameters A=0.02, p=k=3 is
How did you take the first derivative of the surge function? I'm not quite sure how to take the derivative of the function because it has three variables and my derivative isn't coming out the same as yours for the first or second derivative.
An inflection point on the graph of a function y=f(x) is defined as a point at which the graph passes from one side of its tangent line to another. At an inflection point, the graph changes the direction of its convexity. If the second derivative at some x0 is equal to zero and second derivative changes sign as x passes through x0, then (x0, f(x0)) is an inflection point.
What is the significance of the points of inflection?