Question

Indicate (i.e. check) all labeled points at which f(x) and f′(x) are both nonzero of the same sign.

Select all labeled points at which it would be possible for exactly one of f′(x) and f″(x) to be negative.

Step 1

*Part 1:*

From the given graph, it is observed that the graph is increasing on the intervals

(*A, C*) and increasing after the point *F *then the first derivative of the function is positive.

That is, the interval (*A, C*) and after the point *F* is positive.

Step 2

Here, it is observed that the point *B* is lies on the interval (*A, C*) and the points *B* is positive.

Similarly, the graph is decreasing on the intervals (*C, F*) then the first derivative of the function is negative.

That is, the point *D*, *E *and *F* ...

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Sorry about that. What wasn’t helpful?