The graph of f is shown.Graph f,f ' and f '' on the same set of coordinate axes.

A)
B)
C)
D)
E) none of the above

Question

​The graph of f is shown.Graph f,f ' and f '' on the same set of coordinate axes. ​
​  ​
A) ​ 
B) ​ 
C) ​ 
D) ​ 
E) ​none of the above

Quizplus · Accepted Answer

The graph of f shows that it is a quadratic function with a minimum point at (2,-2). Therefore, the graph of f' has a zero slope at x=2 and is negative to the left and positive to the right of x=2. This gives us a V-shaped graph for f'. Additionally, the graph of f'' is a constant since f' is a linear function. Therefore, the graph of f'' is just a horizontal line passing through (2,0).

Choice A is incorrect because it shows f'' as decreasing on both sides of x=2, which is not true since f'' is constant. Choice B is incorrect because it shows f'' as having a local maximum at x=2, which is not true since f'' is constant. Choice D is incorrect because it shows f'' as having a local minimum at x=2, which is not true since f'' is constant. Therefore, the correct choice is C.

​The Graph of F Is Shown

The Graph of F Is Shown