Al Muizzuddin F

Matematika Ekonomi Lanjutan 2013

Find the slope of a straight line given any two points on theline.

Detect whether a line is uphill, downhill or horizontal usingthe sign of the slope.

Recognize the notation f ′(x) and dy/dx for the derivative ofa function.

Estimate the derivative of a function by measuring theslope of a tangent.

Differentiate power functions.

6/28/2016 al muiz 2

Slope

Garis lurus/ linear

Garismelengkung/ non linear

6/28/2016 al muiz 3

Find the slope of the straight line passing through:(a) A (1, 2) and B (3, 4)(b) A (1, 2) and C (4, 1)(c) A (1, 2) and D (5, 2)

6/28/2016 al muiz 4

6/28/2016 al muiz 5

6/28/2016 al muiz 6

6/28/2016 al muiz 7

Find the slope of the straight line passing through:(a) E (−1, 3) and F (3, 11)(b) E (−1, 3) and G (4, −2)(c) E (−1, 3) and H (49, 3)

6/28/2016 al muiz 8

From these examples we see that the gradient is positive ifthe line is uphill, negative if the line is downhill and zero ifthe line is horizontal.

Unfortunately, not all functions in economics are linear, so itis necessary to extend the definition of slope to includemore general curves. To do this we need the idea of atangent, which is illustrated in Figure 4.4.

A straight line which passes through a point on a curve andwhich just touches the curve at this point is called atangent

6/28/2016 al muiz 9

6/28/2016 al muiz 10

6/28/2016 al muiz 11

Slope garis lurus:o Memiliki kemiringan yang tetap

Slope garis melengkung:o Memiliki kemiringan yang berubah-ubah

6/28/2016 al muiz 12

6/28/2016 al muiz 13

However, as we have just seen, the slope of a curve variesas we move along it. In mathematics we use the symbol

6/28/2016 al muiz 14

6/28/2016 al muiz 15

However, it is important to realize that dy/dx does not mean‘dy divided by dx’. It should be thought of as a single symbolrepresenting the derivative of y with respect to x.

6/28/2016 al muiz 16

6/28/2016 al muiz 17

6/28/2016 al muiz 18

The corresponding graph of the square function is sketchedin Figure 4.7. From the graph we see that the slopes of thetangents are

6/28/2016 al muiz 19

6/28/2016 al muiz 20

6/28/2016 al muiz 21

6/28/2016 al muiz 22

6/28/2016 al muiz 23

Lebih lanjut..

6/28/2016 al muiz 24

6/28/2016 al muiz 25

6/28/2016 al muiz 26

6/28/2016 al muiz 27

6/28/2016 al muiz 28

6/28/2016 al muiz 29

6/28/2016 al muiz 30

6/28/2016 al muiz 31

6/28/2016 al muiz 32

Kerjakan Soal Latihan Halaman249-250, buku Jacques (2006),untuk Nomor: 5, 9, 10, 12, dan 13Minggu depan dikumpulkan, tulis

pada kertas folio garis

6/28/2016 al muiz 33