The problem asks you to sketch a possible graph of the function f(x) on the same grid, given that the graph provided is the derivative f'(x). Here's how you can reason through the sketch:

Key Concepts:

1. Critical Points: These occur where f'(x) = 0. At these points, f(x) could have a local maximum, local minimum, or an inflection point.
2. Increasing/Decreasing Behavior:
   • Where f'(x) > 0, the function f(x) is increasing.
   • Where f'(x) < 0, the function f(x) is decreasing.
3. Concavity:
   • Where f'(x) is increasing (i.e., the slope of f'(x) is positive), f(x) is concave up.
   • Where f'(x) is decreasing (i.e., the slope of f'(x) is negative), f(x) is concave down.

Analyzing the Graph of f'(x):

1. Intervals of Increase and Decrease:

   • For x < -2, f'(x) < 0: f(x) is decreasing.
   • From x = -2 to x = 1, f'(x) > 0: f(x) is increasing.
   • For x > 1, f'(x) > 0 but increasing rapidly: f(x) continues to increase.

2. Critical Points:

   • At x = -2 and x = 1, f'(x) = 0: These are critical points where f(x) might have a local minimum or maximum, or possibly an inflection point.

3. Concavity:

   • From x = -3 to x = -1, f'(x) is increasing (positive slope), so f(x) is concave up.
   • From x = -1 to x = 0, f'(x) is decreasing (negative slope), so f(x) is concave down.
   • From x = 0 to x = 4, f'(x) is increasing rapidly, so f(x) is concave up.

Steps to Sketch f(x):

1. Start at x = -3: Since f'(x) < 0, f(x) is decreasing. Draw a decreasing curve.
2. At x = -2: f'(x) = 0, so f(x) reaches a local minimum. Start increasing the curve after this point.
3. From x = -2 to x = 1: f(x) is increasing, but note the concavity changes at x = -1 from concave up to concave down.
4. At x = 1: f'(x) = 0, and after this point, f(x) continues to increase. The function f(x) starts to curve upward more sharply due to the increasing derivative.
5. Beyond x = 1: f(x) continues to increase rapidly and is concave up.

You should draw the graph accordingly on the same grid, with the key points and behavior in mind. The sketch will likely show a smooth curve that reflects the transition in the behavior of f(x) based on the analysis above.