Particle A and B moves relative to each other in an x-y coordinate system. The positions of particle A and B as a function of time are (1... 繼續閱讀

求解21,22,38🙇 section1.3不用理他 equation 2.1.5是微分的定義式

Z (b) Use the acceleration curve from par (a) to estimate the 10 seconds. What are the units for jerk? 45) The lel defined ||||| V has a vertical tangent line at (0,0). and jerk at = 38, Let f(x) = V. x ( (a) If a 40. use Equation 2.1.5 to find s'a). (b) Show that f'(o) does not exist. (c) Show that y- (Recall the shape of the graph of f. See Figure 1.2.13.) 39. (a) If g(x) = x?, show that g'(0) does not exist. (b) Ifa * 0, find g'(a). (c) Show that y = x2 has a vertical tangent line at (0,0). c (d) Illustrate part (c) by graphing y - x2) if the sided (a) F | 40. Show that the function f(x) = |x - 6 is not differentiable at 6. Find a formula for and sketch its graph. (b) Where is the greatest integer function () = [x] not

求解21,22,38🙇 section1.3不用理他 equation 2.1.5是微分的定義式

(d) Use the definition of derivative to prove that your guess in part (c) is correct. 14-21 Find the derivative of the function using the definition of derivative. State the domain of the function and the domain of its derivative. 14. f(x) = 3x - 8 15) f(x) = mx + b 16. f(x) - 4 + 8x - 5x? (17) f(x) = x - 3x + 5 18. f(x) - x + V g(x) - 19- x? - 1 20. f(x) 21s(x) x2 2.x - 3 (hours) arger. The graph hat the battery purs). (r)? graph - a 22.) a) Sketch the graph of f(x) - V6 - x by starting with the graph of y # and using the transformations of Section 1.3. (b) Use the graph from part (a) to sketch the graph of f! (c) Use the definition of a derivative to find f'(x). What are the domains of f and f'? (d) Use a graphing device to graph f' and compare with your sketch in part (b). lo-TE 23. (a) If f(x) = x + 1/x, find f'(x). (b) Check to see that your answer to part (a) is reasonable by JE comparing the graphs of f and f'. 1 (hours) shows how 24. The table given tho hai

不知道這個怎麼算🥲

Section 3.5 39. Do the graphs of the functions in Exercises 39-42 have any horizontal tangents in the interval 0 5x = 27? If so, where? If not, why not? Visualize your findings by graphing the functions with a grapher. 39. y = x + sin. ANS: Yes. At x = TT

1 跟2都看懂了 可以問一下為什麼第三題是這樣嗎？謝謝！

(1 point) Suppose f'(x) is a differentiable decreasing function for all x. In each of the following pairs, which number is the larger? For each, enter A or B. 1. Comparing A. f'(8) and B. f'(9): A is larger 2. Comparing A. f" (8) and B. O: B is larger 3. Comparing A. f(8 + Ax) and B. f(8) + f'(8)Ax: B is larger For each, make sure that you can explain why.

請問35、36怎麼解，希望有算式✍🏻，感謝！

b. What is the rate of change of the total cost when the level of production is ten surfboards a day? 35. EFFECT OF ADVERTISING ON PROFIT The quarterly profit (in thousands of dollars) of Cunningham Realty is given by x in = 3.5, 3. alt of P(x) = -*** + 7x + 30 = -ered en by time = - vhen 1 P( -x2 + (0 < x < 50) 3 bos where x (in thousands of dollars) is the amount of money Cunningham spends on advertising per quarter. a. Find P'(x). b. What is the rate of change of Cunningham's quarterly profit if the amount it spends on advertising is $10,000/quarter (x = 10) and $30,000/quarter (x = 30)? 36. DEMAND FOR TENTS The demand function for Sportsman 5 X 7 tents is given by p = f(x) = -0.1x2 – x + 40 where p is measured in dollars and x is measured in units of a thousand. a. Find the average rate of change in the unit price of a tent if the quantity demanded is between 5000 and 5050 tents; between 5000 and 5010 tents. b. What is the rate of change of the unit price if the quan- tity demanded is 5000? t (b). = own at its 2. time s the

求解21,22,38🙇 section1.3不用理他 equation 2.1.5是微分的定義式

(d) Use the definition of derivative to prove that your guess in part (c) is correct. 14-21 Find the derivative of the function using the definition of derivative. State the domain of the function and the domain of its derivative. 14. f(x) = 3x - 8 15) f(x) = mx + b 16. f(x) - 4 + 8x - 5x? (17) f(x) = x - 3x + 5 18. f(x) - x + V g(x) - 19- x? - 1 20. f(x) 21s(x) x2 2.x - 3 (hours) arger. The graph hat the battery purs). (r)? graph - a 22.) a) Sketch the graph of f(x) - V6 - x by starting with the graph of y # and using the transformations of Section 1.3. (b) Use the graph from part (a) to sketch the graph of f! (c) Use the definition of a derivative to find f'(x). What are the domains of f and f'? (d) Use a graphing device to graph f' and compare with your sketch in part (b). lo-TE 23. (a) If f(x) = x + 1/x, find f'(x). (b) Check to see that your answer to part (a) is reasonable by JE comparing the graphs of f and f'. 1 (hours) shows how 24. The table given tho hai

請問a、b怎麼做 謝謝

(a) If g is a twice differentiable function and f(x) = xg(x?), find f" in terms of g, g', and g". () = If F(x) = f(xf(xf(x))), where f(1) = 2, f (2) = 3, f'(1) = 4, f'(2) = 5, and f'(3) = 6, find F'(1).

第46題 一直不是很確定😅🥺🥺

54. Differentiability and Continuity on an Interval Each figure in Exercises 43–48 shows the graph of a function over a closed interval D. At what domain points does the function appear to be a. differentiable? b. continuous but not differentiable? c. neither continuous nor differentiable? 55 5 Give reasons for your answers. 44. y 43. y = f(x) y D: -3 = x < 2 2t y = f(x) D: -2 < x < 3 2. 1 1H -3 X X -3 -2 -1 0 1 2 -2 -1 - 1 2 3 10 -1 -1 - 27 -27 45. (46. y y y = f(x) D: -3 < x < 3 y = f(x) D: -2<x<3 3 RE w 1 -3-2-10 -1 X -2日 2 1 2 2 -2 -1 01 1 3

請問這三小題要怎麼寫⊙﹏⊙

64. Let f be a function that is differentiable at x = c. noa. Explain why f(x) – f(c) f'(c) = lim X - C - X->C