Section 4.4, Question 86
- a) Note that g'=f so g will achieve a
local maximum at points where f changes from positive to negative.
Likewise, it will have a local minimum at any point where f changes
from negative to positive. So the local maxima occur at x=2,6,10.
Actually x=10 is a little debatable since it depends on our precise
understanding of what it means to be a local maximum. The local minima occur at
x=4,8.
- b) The absolute maximum must occur at one of the local maxima
listed above. Looking at the graph of f, I conclude that
- c) g is concave down on intervals where
g'=f is decreasing. These are the intervals [1,3],
[5,7] and [9,10].
- d)