Change > Derivative values
12345Derivative values

Solutions to the exercises

Exercise 1
a

( Δ y ) ( Δ t ) = ( 4 , 9 5 2 - 4 , 9 0 2 ) ( 5 - 0 ) = 24 , 5 m/s

b

49 m/s

c

The rock reaches the ground after approximately 10,1 s. Its velocity is then about 99,0 m/s.
That is nearly 356 km/h!

Exercise 2
a

f ' ( 2 ) = 8

b

The function is increasing at x = 2 .

c

y = 8 x - 4

Exercise 3
a

g ' ( 1 ) = - 4

b

Point ( - 1 , 4 ) . The graph is point symmetric to the origin ( 0 , 0 ) .

c

There is no slope at that point. The graph has a vertical asymptote at x = 0 .

Exercise 4
a

The function shows a decelerating decrease.

b

Approximately 1,18 g/hour

c

- 0,62 g/hour

Exercise 5
a

Approximately ( 5 , 6 ) 5 = 1 , 12 m/year

b

Approximately 0,4 m/year

c

At t i m e = 2 years, as the slope of the line is steepest at that point.

d

0 m/year

Exercise 6
a

10

b

tan ( α ) = 10 gives you α 84 °C

c

( 5 , 25 )

d

Point ( 8 , 16 ) and slope - 6 .

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