Question #0a15a
1 Answer

Maximum:
#(0, 1)#
#(2pi, 1)# 
Minimum:
#(pi, 1)#
graph{y = cos(x) [1.315, 7.335, 1.36, 2.966]}
Explanation:
Finding absolute extrema follows exactly the same process as finding relative extrema. The only extra thing is you'll need to is compare the relative extrema, and see which one is the highest/lowest.
Our first step is to find all critical points (i.e. where
So our critical values are
.
Now, we need to test and see which of these is the biggest/smallest.
Important note here: normally we'd also need to test the endpoints of our interval as well. We didn't need to explicitly do that here since the endpoints were also critical values, but in future problems it's key that you carry out that extra step.
Let's test!
Now, what's your largest value? Well, that's
What's your smallest value? That's just going to be
In coordinates, your absolute extrema are:

Maximum:
#(0, 1)#
#(2pi, 1)# 
Minimum:
#(pi, 1)#
Take a look at the graph of
graph{y = cos(x) [1.315, 7.335, 1.36, 2.966]}
You may wonder: how can
Hope that helped :)