Applying

Rates of

Change in

Real-life

SituationsKen

SimerNaufal

NicholasAdam

“research” slides

Definitions

Polynomial function – a function with a degree of more than 1

Preceding interval – the interval chosen between the point of interest and one before it to calculate the approximate instantaneous rate of change

Following interval – the interval chosen between the point of interest and one after it to calculate the approximate instantaneous rate of change

Centred interval – the interval chosen between one point before and one point after the point of interest to calculate the approximate instantaneous rate of change

Instantaneous rate of change – the exact rate of change calculated at one point

Average rate of change – the approximate rate of change calculated between 2 points

Secant line – the line that connects 2 points on a graph and whose slope gives the average rate of change between the 2 points

Tangent line – the line that only touches the graph at 1 point and whose slope gives the instantaneous rate of change at that point

age of men, xnumber of days of

intercourse in a month, y0 05 0

10 015 020 125 1230 1635 1440 1045 750 355 260 165 0

20-25 => 12-1 = 2.5 5

40-45 => 7-10 = - 0.6 5

50-55 => 2-3 = -0.2 5

Interval 1

Interval 2

Interval 3

Increasing rapidly

decreasing rapidly

decreasing slowly

Average rate of change

30-35 => 14-16 = - 0.4 35-30

Instantaneous rate of changeat x = 25

35-40 => 10-14 = - 0.8 40-35

30-35 => 10-16 = - 0.6 40-30

Preceding interval

Following interval

Centred interval

Higher rate of change

Lower rate of change

Intermediate rate of change

0 10 20 30 40 50 60 700

2

4

6

8

10

12

14

16

18

f(x) = − 6.508427932575E-08 x⁶ + 1.270953401603E-05 x⁵ − 0.000904359503585 x⁴ + 0.02787284670953 x³ − 0.338748286629038 x² + 1.25552353735018 x − 0.086687306504978R² = 0.940469063820321

number of days of intercourse in a monthPolynomial (number of days of intercourse in a month)

num

ber o

f day

s of i

nter

cour

sein

a m

onth

age of men

secant line slope

1 16-1/30-20 = 1.5

2 15.6-4.4/29-22 = 1.5

3 15.2-7/28-23 = 1.64

4 14-10/26.5-24 = 1.6

12.01487213 - 12/0.01 = 1.4

12.01646749 - 12/-0.01 = 1.6

1.6 + 1.4/2 = 1.5

Difference of quotient methodat x = 25

Positive: h = 0.01

Negative: h = -0.01

Final:

ThAn

K yOufOr PaYiNg

aTtEnTiOntO oUr akward PrEsEnTaTiOn

:P