Do I need to find the graph of f in order to find the answer to the attached problem?! Please help with a full description of how the answer was achieved!

Regarding the graphed function, we have that:

a. The critical points are given as follows:

b. The function is concave up and decreasing on the intervals (-3,-2) U (0,1), as the first derivative is both negative and increasing on these intervals.

c. The inflection points are x = -2, x = 0 and x = 2.

The critical points of a function are the points in which the derivative is of 0, and can be classified as maximum or minimum, as follows:

We are given the graph of the derivative, hence the zeros are the critical points, as follows:

The points of the inflection of a function are the points in which the second derivative is of zero.

We are given the graph of the first derivative, hence the inflection points are where the graph changes from increasing to decreasing or decreasing to increasing, as follows:

x = -2, x = 0 and x = 2.

The curve is classified as concave up or concave down as follows:

The first derivative is increasing in these following intervals:

(-3, -2) U (0,2).

Meaning that the function is concave up on this interval.

The function is decreasing when the first derivative is negative, hence the interval is:

(-3, 1) U (3, 4).

The intervals in which the first derivative is both negative and increasing are:

(-3,-2) U (0,1).

Which are the intervals in which the function is both concave up and decreasing.

More can be learned about functions at https://brainly.com/question/28041013

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