Given the numerical values shown for the function f(x), find approximate values for the derivative of f(x) at each of the x-values given.

x= 0 1 2 3 4 5 6 7 8
f(x)= 13 15 16 17 17 14 11 9 7
f'(x)= 2 1 1 1 0 -3 -3 -2 -2

What seems to be the greatest rate of change of f(x)?
rate of change = _______

The task was to find f'(x), which I already did... but I thought that theh greatest rate of change was -3... how can I get the greatest rate of change???

Forget it... it's 2.. don't know why I thought it was -3 thanks anyways...

thank you for trying!

Well, when it comes to finding the greatest rate of change, or the maximum rate of change, it's important to look for the steepest slope. In this case, the values of f'(x) indicate the rate of change of f(x) at each x-value. The greatest rate of change corresponds to the steepest positive slope.

Looking at the values you provided for f'(x), we can see that the greatest rate of change occurs at x=0, where the derivative is 2. Therefore, the greatest rate of change of f(x) is 2.

Now, I know some may think that -3 might be the greatest rate of "decrease", but when talking about the "greatest rate of change," it refers to both increasing and decreasing rates. So, in this case, 2 is the answer!

To find the greatest rate of change of f(x), you need to determine the maximum value of f'(x). From the values given for f'(x) at each x-value, the greatest rate of change is -3. Negative values indicate a decreasing function, so the greatest rate of change of f(x) is -3. Therefore, the greatest rate of change is -3.

To find the greatest rate of change of the function f(x), we need to determine the maximum value among the list of derivative values, f'(x).

Looking at the provided values of f'(x): 2, 1, 1, 1, 0, -3, -3, -2, -2; we can see that the greatest rate of change occurs when f'(x) is -3.

Hence, the greatest rate of change of f(x) is -3.

To obtain this result, you found the derivative of f(x) correctly, which gave you the values for f'(x). Then, you determined the maximum value from the list of derivative values, which corresponds to the greatest rate of change in f(x).