Please solve all and justify where needed.

2. The function f (x) is twice differentiable with selected values of f, f', and f" given in the table below. Which of the following correctly identify the location of any relative extrema on the graph of f (x). X 2 5 f(x) 9 7 3 f'(x ) 3 0 f "(x) -6 4 0 (A) relative maximum at x = 2 (B) relative maximum at x = 2 relative minimum at x = 7 f (x) has no relative minimum (C) relative maximum at x = 7 (D) f (x) has no relative maximum relative minimum at x = 2 relative minimum at x = 7 3. The data in the chart below shows all the critical numbers of the differentiable function, f (x) , along with its first and second derivative values near those critical numbers. What can be determined about the points of inflection of f? x -8 -6 - 4 -2 0 2 4 6 8 f (x) - 2 8 6 0 -6 -8 2 f' (xx) 12 0 -3 -2 0 -2 -4 0 10 f "(x) -14 -3 0 0 0 4 12 (A) There are points of inflection at x = -6, x =0, and x = 6. (B) There are points of inflection at x = -6, and x = 6 (C) There is a point of inflection at x = 0. (D) There are points of inflection at x = -4, x =0, and x = 4. 4. The figure to the right shows the graph of f' , the derivative of the function f. The graph of f'(x) has horizontal tangent lines at x= -1, x = 1 and x = 3. a. For what value(s) of x does fhave a relative minimum? Justify. b. For what value(s) of x does fhave a relative Note: This is the graph of the derivative of f, not the graph of J . maximum? Justify. c. On what interval(s) is the graph of / concave upward? Justify