Thomas Calculus 13th [Solutions]

Chapter 4 Practice Exercises 319
12. The absolute maximum is | 1| 1 and the absolute minimum is |0| 0. This is not inconsistent with the
Extreme Value Theorem for continuous functions, which says a continuous function on a closed interval attains
its extreme values on that interval. The theorem says nothing about the behavior of a continuous function on an
interval which is half open and half closed, such as [ 1,1), so there is nothing to contradict.
13. (a) There appear to be local minima at x 1.75
and 1.8. Points of inflection are indicated at
approximately x 0 and x 1.
(b)
(c)
7 5 4
f ( x) x 3x 5x
indicates a local maximum at
2 2 2 3
15 x x ( x 3)( x 5). The pattern
x 3 5 and local minima at x 3.
y
|
3
| | |
0
3
5 3
14. (a) The graph does not indicate any local
extremum. Points of inflection are indicated
at approximately x 3 and x 1.
4
(b) f ( x) x 7 2x
4 5 10
3
x
local maximum at
(c)
3 3 7
x ( x 2)( x 5). The pattern
x 7 5 and a local minimum at
x
3 2.
f
)( |
0
7
5
| indicates a
3 2
Copyright
2014 Pearson Education, Inc.