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
1
0
-1
-6
-8
2

f'(x)
12
0
-3
-2
0
-2
-4
0
10

f''(x)
-14
-3
0
1
0
-1
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.

Question

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
1
0
-1
-6
-8
2


f'(x)
12
0
-3
-2
0
-2
-4
0
10


f''(x)
-14
-3
0
1
0
-1
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.

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x	-8	-6	-4	-2	2	4	6	8
f(x)	-2	8	6	1	-1	-6	-8	2
f'(x)	12	0	-3	-2	-2	-4	0	10
f''(x)	-14	-3	0	1	-1	0	4	12