1 / 15

C H A P T E R 2

C H A P T E R 2. Differentiation: Basic Concepts. Figure 2.1 The graph of s = 16 t 2 . (a) The secant line through P (2, 64) and Q (2 + h , 16(2 + h ) 2 ). (b) As h  0, the secant line PQ tends toward the tangent line at P . 2-1-51.

kiaria
Télécharger la présentation

C H A P T E R 2

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. C H A P T E R 2 Differentiation:Basic Concepts

  2. Figure 2.1 The graph of s = 16t2. (a) The secant line through P(2, 64) and Q(2 + h, 16(2 + h)2). (b) As h0, the secant line PQ tends toward the tangent line at P. 2-1-51

  3. Figure 2.2 Secant lines approximatinga tangent line. (a) The graph of f(x) with a secant line through points P(x, f(x)) and Q(x + h, f(x + h)). (b) As h0 the secant lines tend toward the tangent line at P. 2-1-52

  4. Figure 2.3 Inflation as a functionof unemployment Source: Adapted from Robert Eisner, The Misunderstood Economy:What Counts and How to Count It, Boston, MA: Harvard Business School Press, 1994, page 173. 2-1-53

  5. Figure 2.4 The graph of y = x3. 2-1-54

  6. Figure 2.5 The graph of R(x) = 0.5x2 + 3x – 2, for x 0. 2-1-55

  7. Figure 2.6 Three functions that are not differentiable at (0, 0). (a) The graph has a gap at x = 0. (b) There is a sharp “corner” at (0, 0). (c) There is a “cusp” at (0, 0). 2-1-56

  8. Figure 2.7 The graph of f(x) = c. 2-2-57

  9. Figure 2.8 The motion of a ball thrown upward from the top of a building. 2-2-58

  10. Figure 2.9 Marginal cost MC(x0) approximatesC(x0 + 1) – C(x0). (a) The marginal cost MC(x0) at x = x0 is C’(x0). (b) The cost of producing the (x0 + 1)th unit is C(x0 + 1) – C(x0). 2-4-59

  11. Figure 2.10 The graph of the profit function display function 2-4-60

  12. Figure 2.11 Approximation of y by the differential dy. 2-4-61

  13. Figure 2.12 The graph of the circle x2 + y2=25. 2-7-62

  14. Figure 2.13 The graph of the equationx2 – y2 = 2x + 2y. 2-7-63

  15. Figure 2.14 A ladder moving down a wall. 2-7-64

More Related