What does the Second Derivative Test tell you about the behavior of f at these critical numbers?

Question

What does the Second Derivative Test tell you about the behavior of f at these critical numbers?

From Part (a), we have three critical numbers: x = 0

, x = 20/7

, and x = 4.

At x = 0

, f  ---Select--- has a relative minimum value has a relative maximum value does not have a relative extremum value may or may not have a relative extremum value because  ---Select--- f '' does not change sign at x = 0 f '' changes sign from - to + at x = 0 f '' changes sign from + to - at x = 0 f '' (0) is positive f '' (0) is negative f '' (0) = 0 or DNE .

At x = 20/7

, f  ---Select--- has a relative minimum value has a relative maximum value does not have a relative extremum value may or may not have a relative extremum value because  ---Select--- f '' does not change sign at x = 20/7 f '' changes sign from - to + at x = 20/7 f '' changes sign from + to - at x = 20/7 f '' (20/7) is positive f '' (20/7) is negative f '' (20/7) = 0 or DNE .

At x = 4

, f  ---Select--- has a relative minimum value has a relative maximum value does not have a relative extremum value may or may not have a relative extremum value because  ---Select--- f '' does not change sign at x = 4 f '' changes sign from - to + at x = 4 f '' changes sign from + to - at x = 4 f '' (4) is positive f '' (4) is negative f '' (4) = 0 or DNE .

Answer 1

I would need to see Part a) to help with this question.