Question

Find the possibility graph of its derivative f'.

Short answer

The possibility graph of its derivative f' is

Step-by-step solution

Step 1. Given

The given information is

Step 2. Explanation

From the above graph the function is decreasing on (- ∞, 0) where f^ prime <0 and increasing at (0, ∞) where f' prime >0 . Therefore, the possible graph of the derivative of above graph is shown below:

The graph of f' prime have roots at x = 0 and x = 2 . The graph of f^ prime should "bounce" off the x axis at x = 2