A critical point is defined as a point where the derivative is equal to 0.
So if it defined y = f'(x) your critical points would be wherever f'(x) = 0, simple as that!
The following table gives values of the differentiable function y=f(x).
x: 0 1 2 3 4 5 6 7 8 9 10
y: 2 1 -1 2 5 3 -2 1 4 7 10
For the first part of the question, I found the critical points and identified them as local max/min. The answers were: (2,min),(4,max),(6,min).
The part I'm having trouble with is as follows:
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).
How would my answers change? How would I determine what the critical points were for the derivative and whether they are max/min?