Maxima and minima

We can clearly see the blue graph, it is the locus of a function \[f(x)=y= ax^3+bx^2+cx+d\] . We can change the values of a, b, c and d using their respective slide bars. Point A lies on the function f(x) and a tangent (pink line) is drawn at this point. We can move the point A. m is the slope of the tangent
Question/s to think about. 1. What is the case when m=0? 2. What is the value of m when A is at the local maxima or local minima of the function? 3. Set the values of a, b, c and d as a=0.6, b=1, c=0.5 and d=2. What do we observe?