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12345Difference quotient

Solutions to the exercises

Exercise 1
a

( Δ y ) ( Δ x ) = 2 1 = 2

b

- 2 3

c

D and F and A and E .

d

The difference quotient is negative.

Exercise 2

4 2 = 2

Exercise 3
a

( 2 - 6 ) ( 2 - 0 ) = - 2

b

0

c

The points are equally high; they have the same y -value.

d

E.g. using [ - 1 , 0 ] with ( Δ y ) ( Δ x ) = ( 6 - 2 ) 1 = 4

Exercise 4
a

t = 0 gives T = 90 °C.

b

( Δ T ) ( Δ t ) = ( T ( 5 ) - T ( 0 ) ) ( 5 - 0 ) ( 45 , 95 - 90 ) 5 - 8 , 8 °C/min.

c

About 3,3°C/min.

d

The difference quotients get smaller; the coffee cools off more slowly because the difference to the surrounding temperature becomes smaller.

Exercise 5

( Δ y ) ( Δ x ) = ( 3 ( a + 1 ) 2 - 3 a 2 ) 1 = 6 a + 3

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