I have inverse third order that have equation y=y0+a/x+b/x2+c/x3. usually the slope, for example cubic function equation y=y0+ax+bx2 + cx3 is taken from the constant with a with x degree of 1. so, for the inverse equation, is the slope can be calculated from constant a also?
The definition of slope is the change in y coordinate divided by the corresponding change in x coordinate. That is slope = dy/dx. You can obtain constant slope values for the linear function, not for the non-linear functions. So, the slope varies along the curve. In your case, at first you have to compute dy/dx and then you have to apply a particular point (say x = 4 or (3,2)), then you will get the corresponding slope value.
Any differential calculus book would help you further.
Just differentiate it and obtain for x≠0 that
y'=dy/dx=-a/x^2-(2*b)/x^3-(3*c)/x^4
The geometric mean to the first derivative at some point on a function graph is the slope of the tangent at that point, in other words,slope = tan(theta) where "theta" is the angle between that tangent line and x-axis opposite to clock direction. For the case of a line the slope at any point is constant = tan(theta) where theta is the angle between that line and x-axis, so it is easy to find it without plotting this function, by differentiating the function to give directly the coefficient of the variable x, but in higher order polynomials the tangent change it's angle with x-axis from point to another on the function curve, so the direct way to know the slope at any point is to differentiate this function with respect to x, which gives the slope at any point on the curve, then substitute with the fixed point x0 into that derivative to find the slope at it.
see the attached formula for your function.
Best luck.
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