Please show your work.

7. (1 point) (incorrect) Similar to 4.1.30 in Rogawski/Adams. 8. (1 point) The stopping distance for an automobile (after applying the Similar to 4.1.34 in Rogawski/Adams. brakes) is approximately F(s) = 1.1s + 0.054s ft, where s is the speed in mph. Use the Linear Approximation to estimate The resistance R of a copper wire at temperature T = 30C the change in stopping distance per additional mph when s = 60 is R = 1502. Estimate the resistance at T = 31 C, assuming that and when s = 80. dR The change in stopping distance per additional mph for s = dT T=30 = 0.0402/C 60 mph is approximately - ft. Give your answer to at least three decimal places. R(31) ~ The change in stopping distance per additional mph for s = 80 mph is approximately ft. Give your answer to at least three decimal places. Answer(s) submitted: Answer(s) submitted: (incorrect) Generated by WeB Work, http:/webwork.maa.org, Mathematical Association of AmericaRex Wu $22M171 Assignment 4.3 due 04/06/2022 at 08:00pm MDT 1. (1 point) 3. (1 point) Similar to 4.3.2 in Rogawski/Adams. Similar to 4.3.15 in Rogawski/Adams. Find a point c satisfying the conclusion of the Mean Value Determine the intervals on which f' (x) is positive and neg- Theorem for the following function and interval. ative, assuming the figure below is the graph of the function f and has a domain of (-0o, 6). f(x) = vx on the interval [16, 64] Answer(s) submitted: (incorrect) 2. (1 point) Similar to 4.3.13 in Rogawski/Adams. Interval(s) where f' (x) is positive: If more than one interval, use U for a union. Let f(x) = 13+x2. Interval(s) where f' (x) is negative: If more than one interval, use U for a union. Answer(s) submitted: (incorrect) 4. (1 point Similar to 4.3.16,17 in Rogawski/Adams. Determine the interval(s) on which f is increasing or decrease ing and determine the critical point(s) for f and classify them as local min, local max or neither, assuming the figure below is the graph of the DERIVATIVE of f. Note that the domain of f is all real numbers and that all critical points are showing. The secant line between x = 0 and x = 1 has slope m =_ So by MVT, there is a c for some point c E (0, 1) where f (c) = m. Estimate the x- coordinate of c of the point of tangency. X~. Note: If you click on the graph and hold, you can slide around the graph to align the line with the graph. Answer(s) submitted: (incorrect) This graph represents the DERIVATIVE of f.Interval(s) where f is increasing: interval, use U for a union. If more than one Answer(s) submitted: Interval(s) where f is decreasing: one interval, use U for a union. If more than The smallest critical point x = is a ? The middle critical point x is a ?. The largest critical point: x = is a ? If you don't get this in 3 tries, you can get a hint. Answer(s) submitted: (incorrect) 7. (1 point) Similar to 4.3.39 in Rogawski/Adams. Find the critical point(s) and determine if the function is increas ing or decreasing on the given intervals. y = 3x + 8x-1 (x> 0) Critical point: c = - (incorrect) 5. (1 point) The function is: Similar to 4.3.25 in Rogawski/Adams. 2 on (0, c). 2 on (c, 00 ) . Find the critical point(s) for f (x) = x43 and use the First De- rivative Test to determine whether they are local minimum, local Answer(s) submitted: maximum or neither. The smallest critical point x = is a ? . The largest critical point x is a ? . Answer(s) submitted: (incorrect) 8. (1 point) Similar to 4.3.41 in Rogawski/Adams. Find the critical point and the interval on which the given function is increasing or decreasing, and apply the First Deriva- (incorrect) tive Test to the critical point. Let 6. (1 point) 10 f ( x) = - Similar to 4.3.28 in Rogawski/Adams. * 2 + 5 Critical Point = Find the critical point(s) and the interval on which the given Is f a maximum or minumum at the critical point? ? function is increasing or decreasing, and apply the First Deriva- The interval on the left of the critical point is tive Test to each critical point. Let On this interval, f is ? while f' is ? f(x) = 9x2 + 4x-3 There is only one critical point. If we call it c, then The interval on the right of the critical point is. On this interval, f is ? while f' is ? Is f a maximum or minumum at the critical point? Answer(s) submitted: At c, f is ? The critical point gives us two intervals. The left-most interval is and on this interval f is ? while f' is ? The right-most interval is On this interval f is ? while f' is ? (incorrect) Generated by WeB Work, hilp://webwork.maa. Mathematical Association of America