How do you use the important points to sketch the graph of #y = x^2 - x + 5#?
1 Answer
They identify where the equation makes turns, and in which direction.
Explanation:
The point of "using important points to sketch" is that you don't need to calculate the actual curve, point-by-point if you only want to see a general trend.
The critical information from a curve is usually its direction and magnitude - where does it go, and how quickly? For this we can use the first and second derivatives to find the inflection points. With a "zero" (or two) and the inflection points (which may be minima, maxima, or just a change in the slope direction) we can approximate the shape and location of a curve.
For previously posted details on the process, search for the keywords "First Derivative", "Second Derivative", "Local Maximum" and similar ones on this Socratic site.
