Question

The following table gives values of a differentiable function y= f(x). x: 0 1 2 3 4 5 6 7 8 9 10. y:-1 2 3 2 -2 1 2 3 5 6 8. Now assume that the table gives values of the continuous function y=f'(x) (instead of f(x)). Estimate and classify critical points of the function f(x) as either min, max, or neither.

Answer 1

First thing to do with this problem is to plot the given data in MS excel. We can see in the graph that the minima (lowest point of the graph) is at (4,-2) and the maxima is at (2,3). The critical points are points which the direction changes from one side to another.