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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.

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C H A P T E R 2

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  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

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