Changes

Exercise 1

See the graph of a certain function.
Write down the following

the intervals where the curve is decreasing, where the curve is increasing and the type of decrease or increase;
the extreme values;
for which values of `x` the rate of increase or decrease is largest.

Exercise 2

Given is the function with description $y = 18 x - x^{3}$ .

Write down

the intervals where the curve is decreasing, where the curve is increasing and the type of decrease or increase;
the extreme values;
for which values of $x$ the rate of increase or decrease is largest.

Exercise 3

Given is the function $y = 0, 5 \cdot x^{4} - 4 \cdot x^{2} + 8$ .

a

You can look at the graph of this function on your graphic calculator. What are the extreme values of this function?

b

There is exactly one interval on which the function is increasingly decreasing. What is this interval?

Exercise 4

This is a graph of a parachute jump from a height of $3500$ meter. The jumper first goes into free fall and then opens his parachute.

a

After how many seconds did the jumper open his parachute? How can you tell from the graph?

b

During freefall the curve shows an accelerated descent. What does this mean for the speed of falling?

c

When the parachute is open, the speed of falling is constant. How can you tell from the graph? What is the speed of falling once the parachute is open?

Exercise 5

On a certain day the temperature $T$ in °C behaves as follows:

at 6:00 am ( $t = 6$ ) the temperature was $T = 2$ °C;
it is increasingly increasing from $t = 6$ until $t = 12$ ;
it is decreasingly increasing from 12:00 am to 2:30 pm and increasingly decreasing from $t = 20$ ;
it is decreasingly decreasing from $t = 20$ until the end of the day.

Make a sketch of the possible graph of this function and explain at which values of $t$ the function $T$ must have extreme values.

Exercises