- #1
veravarya
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Homework Statement
I have 12 x,y data points (x is distance, y is elevation) divided into three groups (sets). From those three sets, I created 3 cubic polynomials of exact fit, and now I am supposed to find their difference quotients, graph the difference quotients, and use the graph to figure out where the slope is greatest. h is supposed to equal 0.1 so that it's small enough to be almost tangent instead of secant (0.1 is small compared to the data I'm working with, which is in the thousands). I figured out the three difference quotients, but they are all quadratic functions and I don't know how to figure out the slope of those and I don't know understand what the graph should look like.
Homework Equations
difference quotient [itex]= \frac{f(x+h) - f(x)}{h}[/itex]
generic cubic polynomial [itex]= ax^3 + bx^2 + cx + d[/itex]
diff. quot. from gen. cub. poly. [itex]= ah^2 + 3ax^2 + 3ahx +2bx + bh + c[/itex]
The Attempt at a Solution
I tried using the X (distance) data points as inputs into their difference quotient equations and got their respective Y-values, but the scatter plot I made just looks like three different sharp U-shaped pieces. I usually have a very good grasp of things like this but I just don't understand what to do.