Posted by Dan on .
Find the indicated absolute extremum as well as all values of x where it occurs on the specified domain
f(x)= x^2e^-0.25x ; [3,10]
Find f'(x) and see if there is a zero (root) on the interval.
If not, the extrema are the two limits of the interval.
Check the sign of f'(x) on the interval. If there is no zero on the interval, the sign should not change (+ OR -).
If f'(x) is + on the interval, it is monotonically increasing, and vice versa.
If it is monotonically increasing or decreasing, then f(c1) and f(c1) are the limits of the range of the function on the given interval [c1,c2]. I.e. the function does not take up values beyond [f(c1),f(c2)].
Post your answer for checking if you wish.