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Solutions to the exercises

Exercise 1

, - 1 : decreasingly increasing
- 1 , 0 : increasingly decreasing
0 , 1 : decreasingly decreasing
1 , :increasingly increasing
max. y ( - 1 ) 4 and min. y ( 1 ) - 4
In ( 0 , 0 ) the rate of decrease is largest, the slope steepest.

Exercise 2

, - 3 : decreasingly decreasing
- 3 , 0 : increasingly increasing
0 , 3 : decreasingly increasing
3 , : increasingly decreasing
max. y ( 3 ) = 27 and min. y ( - 3 ) = - 27
In ( 0 , 0 ) the increase is fastest, the slope steepest.

Exercise 3
a

There is a maximum for `x=0` and a minimum for `x=-2` and `x=2` .

b

0 , 1

Exercise 4
a

After 60 seconds, because at that point there is a sharp change in speed of descent in the graph. The speed is constant from there onwards.

b

The speed is constantly increasing.

c

The graph is a straight line. v = 1000 / 100 = 10 m/s.

Exercise 5

There is a maximum temperature at 2:30 pm, then the curve goes from increasing to decreasing.

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