Study Guide 1 F_13

# The instantaneous rate of change is a less than 15 b

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Unformatted text preview: B) between 600 and 650 (D) between 700 and 750 (C) between 650 and 700 (E) more than 750 53. Find the instantaneous rate of change of g (t) = 5 − t2 at t = −5. The instantaneous rate of change is (A) less than -15 (B) between -15 and -5 (D) between 5 and 15 (C) between -5 and 5 (E) more than 15 54. Use the formula for instantaneous rate of change, approximating the limit by using smaller and smaller values of h, to ﬁnd the instantaneous rate of change for the function f (x) = 3xx at x = 3. 55. Suppose customers in a hardware store are willing to buy N (p) boxes of nails at p dollars per box, as given by N (p) = 80 − 5p2 ; 1 ≤ p ≤ 4. Find the instantaneous rate of change of demand when the price is \$2. The instantaneous rate of change of demand when the price is \$2 is (A) less than -15 (B) between -15 and -5 (D) between 5 and 15 (C) between -5 and 5 (E) more than 15 56. Use the graph below to estimate the average rate of change of the percentage of new employees from 2000 to 2006. The average rate of change is (A) less than 1% per year (B) between 1% and 2% per year (C) between 2% and 3% per year (D) between 3% and 4% per year (E) more than 4% per year 57. Suppose that the total proﬁt in hundreds of dollars from selling x items is given by P (x) = 2x2 − 7x +5. Answer parts (i) through (iii) (i) Find the average rate of change of proﬁt as x changes from 3 to 5. The average rate of change is (A) less than \$650 per item (B) between \$650 and \$750 per item (C) between \$750 and \$850 per item (D) between \$850 and \$950 per item (E) more than \$950 per item (ii) Find and interpret the instantaneous rate of change of proﬁt with respect to the number of items produced when x = 3. (This number is called the marginal proﬁt at x = 3.) The average rate of change is (A) When items are sold for \$500, the proﬁt is decreasing at the rate of \$3 per item. (B) When items are sold for \$500, the proﬁt is increasing at the rate of \$3 per item. (C) When 3 items are sold, the proﬁt is increasing at the rate of \$500 per item. (D) When 3 items are sold, the proﬁt is decreasing at the rate of \$500 per item. (E) None of these. (iii) Find the marginal proﬁt at x = 5. The marginal proﬁt is (A) less than \$650 per item (B) between \$650 and \$750 per item (C) between \$750 and \$850 per item (D) between \$850 and \$950 per item (E) more than \$950 per item 58. Estimate the slope of the tangent line to the curve at the point (−3, 2). The slope is (A) less than -1 (B) between -1 and 0 (D) between 1 and 2 (C) between 0 and 1 (E) more than 2 59. Use a graphing calculator to ﬁnd f ￿ (3) for the function f (x) = 2ex , if the derivative exists. f ￿ (3) is (A) less than 35 (B) between 35 and 45 (D) more than 55 (C) between 45 and 55 (E) does not exist 60. List the points in the graph in the interval −1 &lt; x &lt; 6 at which the function is not diﬀerentiable. 61. For the function shown in the graph below, answer parts (i) through (iii) (i) Choose the interval(s) on which the rate of chan...
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