Tangent and normal of a function using derivative

We can clearly see the Voilet graph which is of 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). A tangent (orange line) and a normal (blue line) are drawn at this point. m is the slope of the tangent and m1 is the slope of the normal. Coordinates of point A are (x1, y1)
Question/s to think about. Calculate the value of (df(x)/dx)_(〖(x〗_1,y_(1)) )and compare it with m, what do we observe? Calculate the value of -1/(df(x)/dx)_(〖(x〗_1,y_(1)) ) and compare it with m1, what do we observe?