Question

If given a graph of a function's derivative, f'(x), that is defined only between 0 and c. How could I determine the absolute maximum and minimum values as well as the local and max and min values.
At x=0: the function starts high up on the y axis
At x=a: the function crosses the x axis from positive to negative
At x=b: the function goes from negative to 0, but never becomes positive.
At x=c: the function continues to dip down

Thank you

Answer 1

Looks like from the description of the x values, that your absolute max would be at x=0, your local max would be at x=a, local min would be at x=b and your absolute min would be at x=c. This is assuming that the values are from f`(x).

When using real numbers, finding where the derivative is 0 or does not exist will give you points where the slope is 0 and possible critical points for min/max. You can use these numbers, plus the bounds of the interval at which you are looking in the original function to determine the y values, thus giving you your abs min/max and local min/max.

Answer 2

Thank you for your reply, but I am curious as to why x=0 would be the absolute max. And yes the function I described was f'(x), sorry for forgetting to specify that. Since f'(x) starts by decreasing from the y-axis until it hits 0 at point a, wouldn't that make a the local and absolute max?