We have the graph of f(x) in the figure 1.
We have to identify the graph that corresponds to f'(x).
The graph of f(x) is:
Knowing that the first derivative represents the slope of the tangent line, we can see that f'(x) has to be negative for values of x smaller than 0 and positive for values of x greater than 0.
Also, we will have f'(0) = 0, given that we have a minimum there.
The absolute value of f'(x) increases when it approaches to x = 0 from both sides, as the slopes are more steep.
Then, the graph that satisfy this condition is:
Answer: f'(x) is graphed on Graph C.
