Final answer:
To find the minimum and maximum possible values of f(9) - f(3), we need to consider the range of possible values for the derivative of f(x), which is given as 3 ≤ f'(x) ≤ 5. The minimum and maximum values of f(9) - f(3) can be found by considering the minimum and maximum possible values of f(x) between x = 3 and x = 9, which are determined by the slopes 3 and 5, respectively.
Step-by-step explanation:
To find the minimum and maximum possible values of f(9) - f(3), we need to consider the range of possible values for f'(x), which is the derivative of f(x). In this case, we are given that 3 ≤ f'(x) ≤ 5 for all values of x.
Since f'(x) represents the rate of change of f(x), we can interpret this inequality as saying that the slope of the graph of f(x) is between 3 and 5 for all x.
Therefore, the minimum and maximum possible values of f(9) - f(3) can be found by considering the minimum and maximum possible values of f(x) between x = 3 and x = 9, which are determined by the slopes 3 and 5, respectively.