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.

I was able to find the critical points of the original function, which are (2, max) and (4, min); however, I'm having trouble figuring out the critical points of f(x) if thats the graph of f'(x).

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. 

I was able to find the critical points of the original function, which are (2, max) and (4, min); however, I'm having trouble figuring out the critical points of f(x) if thats the graph of f'(x).

anonymous · Answer

i guess you have to estimate where the zeros are, since you are not given any

anonymous · Answer

since $f'(0)=-1$ and also $f'(1)=2$ if you are making the assumption that $f'$ is continuous, it must have a zero between $0$ and $1$

anonymous · Answer

by the same argument it must also have a zero somewhere between 3 and 4