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do these questions P.340 1, 5, 9, 13, 17, 21, 25, 29, 33, 41, 49, 55, 65

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EXERCISES 4.3

=

In Exercises 1 through 38, differentiate the given

function.

1. f(x) = x

3e4r+1

3. f(x)

= xe

2. f(x)

7. f(x) = (x² + 3x + 5) x

8. f(x) = xe

9. f(x) = (1 – 3e)?

10. f(x) = V1 + et

11. f(x) = V3

12. f(x) = x

13. f(x) = Inx

14. f(x) = In 2x

4. f(x)

-0.05x

5. f(x)

= 30 + 10e

=

6. f(x) = 1 + 2-1

=

x

15. f(x) = x? In x

16. f(x) = x InVx

17. f(x) = VA

In x

18. f(x)

x

x +1

19. f(x) = In

VX-1

20. f(x) = e Inx

21. f(x) = {-2x + r?

22. f(t) = In Vt

23. g(s) = (c* + s + 1)(2-3 + s)

24. F(x) = ln(2x – 5x + 1)

+

25. h(t)

Int

26. g(u) = In(u? – 1)

ette

27. f(x)

2

=

1

28. h(x)

=

5

=

29. f(1) = Vint +1

et te

30. f(x)

e -e

31. f(x) = ln(e-* + x)

32. f(s) = 2*+In

33. g(u) = ln(u + Vu? + 1)

x2 + 2x – 3

34. L(x) = In

x2 + 2x + 1

24

35. f(x)

36. f(x) = x+3x

x

41. f(x) = (3x – 1)e for 0 SXS 2

et

e

-2x

42. g(x)

for 0 SX51

2x + 1

43. g(t) = 1/2 -2 for 0 sisi

44. f(x) = e

for 0 Srs1

In(x + 1)

45. f(x)

for 0 SXS 2

x + 1

46. h(s) = 2s In s – 52 for 0.5 SS=2

– 4x

-e

In Exercises 47 through 52, find an equation for the

tangent line to y = f(x) at the specified point

47. f(x) = xe *; where x = 0

48. f(x) = (x + 1)e-2; where x = 0

2x

49. f(x)

where

X=1

22

50. f(x)

In x

=

where x = 1

51. f(x) = x? InVx, where x = 1

52. f(x) = x – In x; where x = e

In Exercises 53 through 56, find the second derivative

of the given function.

53. f(x) = (2x + 2e-1

54. f(x) = ln(2x) + x2

55. f(t) = 2 In

In Exercises 65 through 68, the demand function

q = D(p) for a particular commodity is given in terms

of a price p per unit at which all q units can be sold.

In each case:

(a) Find the elasticity of demand and determine

the values of p for which the demand is

elastic, inelastic, and of unit elasticity.

(b) If the price is increased by 2% from $15,

what is the approximate effect on demand?

(c) Find the revenue R(p) obtained by selling 9

units at the unit price p. For what value of p

is revenue maximized?

65. D(P) = 3,000e -0.04

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Explanation & Answer:

3 Questions

Tags:

algebra

mathematics

calculus

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