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

f'(x) is the slope of f(x) at every x-value. From the graph, we can see that f has a horizontal tangent line at x=-2 and x=4, indicating that f'(x)=0 at these points. At x=-2, the slope changes from negative to positive, indicating that f''(x) is positive at this point. At x=4, the slope changes from positive to negative, indicating that f''(x) is negative at this point. Therefore, we can sketch the graphs of f', and f'' accordingly. The resulting graph aligns with choice B.

The Graph of F Is Shown