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Find the absolute maximum value and the absolute minimum value, if any, of the function. (Round your answers to the nearest integer. If an answer does not exist, enter DNE.) f(x) = x2/3 (x²-4) on [-1, 3] X maximum 5 minimum -3
Maximizing Profits The weekly demand for the Pulsar 40-in. high-definition television is given by the demand equation p=0.07x + 563 (0 ≤ x ≤ 12,000) where p denotes the wholesale unit price in dollars and x denotes the quantity demanded. The weekly total cost function associated with manufacturing these sets is given by C(x) = 0.000002x³ -0.05x2 + 400x + 80,000 where C(x) denotes the total cost incurred in producing x sets. Find the level of production that will yield a maximum profit for the manufacturer. Hint: Use the quadratic formula. (Round your answer to the nearest whole number.) units
Consider the following function. Find the derivative of the function. g'(x) = g(x) = x² - 2x - 6 on [0, 9] Find any critical numbers of the function. (Enter your answers as a comma-separated list. If an answer does not exist, enter DNE.) X = Find the absolute maximum value and the absolute minimum value, if any, of the function. (If an answer does not exist, enter DNE.) maximum minimum
Find the horizontal and vertical asymptotes of the graph of the function. (You need not sketch the graph. Enter your answers as a comma-separated list. If an answer does not exist, enter DNE.) x4 – x2 x(x - 1)(x + 3) f(x) = horizontal asymptote vertical asymptote y = x =
Google's Revenue The revenue for a certain corporation from 2004 (t = 0) through 2008 (t = 4) is approximated by the function R(t) = -0.2t³ + 1.52t² + 1.31t+ 3.7 (0 ≤ t ≤ 4) where R(t) is measured in billions of dollars. (a) Find R'(t) and R"(t). R'(t) = R"(t) = (b) Show that R'(t) > 0 for all t in the interval (0, 4) and interpret your result. Hint: Use the quadratic formula. Setting R'(t) = 0 and solving for t gives t = . (Enter all real number answers, whether or not they fall inside the defined interval. Round your answers to three decimal places. Enter your answers as a comma-separated list.) Both roots lie --Select--- the interval (0, 4). Because R'(0) ?0, we conclude that R'(t)? 0 for all t in (0, 4). (c) Find the inflection point of the graph of R. (Round your answer to two decimal places.) t = Interpret your result. ● The corporation's revenue went was increasing from the start of 2004 until July 2006, and decreasing from that point until the end of 2008. O The corporation's revenue has been stable from the start of 2004 through to the end of 2008. O The corporation's revenue was always decreasing between 2004 and 2008, and decreased fastest in July 2006. O The corporation's revenue was always increasing between 2004 and 2008, and increased fastest in July 2006. O The corporation's revenue went was decreasing from the start of 2004 until July 2006, and increasing from that point until the end of 2008.