QUESTION 1

dy dx Assume x and y are functions of t. Evaluate for 4xy - 3x + 4y" = -76, with the conditions = - 12, dt dt x = 4, y= - 2. dy E dt (Type an exact answer in simplified form.)Find dy for the given values of x and Ax. y= 4x+7;x=2;Ax=0.23 dy = (Round to the nearest thousandth as needed.) Researchers have observed that the mass of a female (gilt) pig can be estimated by the function _ 0.01633(t 124.1) M(t) = - 2.5 +196.7 e where t is the age of the pig (in days) and M is the mass of the pig (in kilograms). a. If a particular gilt is 100 days old, use differentials to estimate how much it will gain before it is 110 days old. b. What is the actual gain in mass? E> a. If a particular gilt is 100 days old, use differentials to estimate how much it will gain before it is 110 days old. It will gain approximately D kilograms. (Do not round until the nal answer. Then round to two decimal places as needed.) b. What is the actual gain in mass? The actual gain in mass is kilograms. (Do not round until the nal answer. Then round to two decimal places as needed.) For the cost and price functions below, nd (a) the number, q, of units that produces maximum prot; (b) the price, p, in dollars per unit that produces maximum prot; and (c) the maximum prot, P, in dollars. - 0.05q. C(q) = 70 + 10qe , p = mi \"'5\" Find the prot function, P. PM) = (a) The number, q, of units that produces maximum prot is q = (Do not round until the nal answer. Then round to the nearest whole number as needed.) (b) The price, p, per unit that produces maximum prot is p = $ (Do not round until the nal answer. Then round to the nearest cent as needed.) (c) The maximum prot is P = $ (Do not round until the nal answer. Then round to the nearest cent as needed.) Suppose that the graph shown is the graph of f'(x), the derivative off(x). Find the open intervals where the original function is concave upward or concave downward. Find any inection points. Find any inection points. Select the correct choice below and, if necessary, ll in the answer box to complete your choice. O A- The original function has (an) inection point(s) at x = (Round to the nearest integer as needed. Use a comma to separate answers as needed.) Q) B. The original function has no inection points. Find the open intervals where the function f is concave upward. Select the correct choice below and, if necessary, ll in the answer box to complete your choice. O A- The original function is concave upward on the interval(s) (Type your answer in interval notation. Use a comma to separate answers as needed.) 6) B. The original function is never concave upward. Find the open intervals where the function f is concave downward. Select the correct choice below and, if necessary. ll in the answer box to complete your choice. O A- The original function is concave downward on the interval(s) (Type your answer in interval notation. Use a comma to separate answers as needed.) G) B. The original function is never concave downward