Answer:
a) The critical points are and
.
b) f is decreasing in the interval
f is increasing in the intervals and
.
c) Local minima:
Local maxima: No local maxima
Step-by-step explanation:
(a) what are the critical points of f?
The critical points of f are those in which . So
So, the critical points are and
.
(b) on what intervals is f increasing or decreasing? (if there is no interval put no interval)
For any interval, if is positive, f is increasing in the interval. If it is negative, f is decreasing in the interval.
Our critical points are and
. So we have those following intervals:
We select a point x in each interval, and calculate .
So
-------------------------
f is decreasing in the interval
---------------------------
f is increasing in the interval .
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f is increasing in the interval .
(c) At what points, if any, does f assume local maximum and minima values. ( if there is no local maxima put mo local maxima) if there is no local minima put no local minima
At a critical point x, if the function goes from decreasing to increasing, it is a local minima. And if the function goes from increasing to decreasing, it is a local maxima.
So, for each critical point is this problem:
At , f goes from decreasing to increasing.
So , f assume a local minima value
At , f goes from increasing to increasing. So, there it is not a local maxima nor a local minima. So, there is no local maxima for this function.