QUESTION 1

Find the absolute extrema if they exist, as well as all values of x where they occur, for the 3 - x 7 + x function f(x) = on the domain [0,7]. 3 - x Find the derivative of f(x) = . 7 + x 10 f' (x) = 2 (7 + X) Select the correct choice below and, if necessary, ll in the answer boxes to complete your choice. '11:? A- The absolute maximum is , which occurs at x = (Round the absolute maximum to two decimal places as needed. Type an exact answer for the value of x where the maximum occurs. Use a comma to separate answers as needed.) C) B. There is no absolute maximum. The total profit P(x) (in thousands of dollars) from the sale of x hundred thousand automobile tires is approximated by P(x) = - x + 9x + 165x -200, x2 5. Find the number of hundred thousands of tires that must be sold to maximize profit. Find the maximum profit. The maximum profit is $ when hundred thousand tires are sold.Find the minimum value of the average cost for the given cost function on the given intervals. C(x) = x3 + 34x +128 (a)15xs10 (b)105x520 (a) The minimum value of the average cost over the interval 1 s x s 10 is (Round to the nearest tenth as needed. Do not include the $ symbol in your answer.) For a certain automobile, M(x) = - 0.015x2 + 1.36x- 7.3, 30 s x s 60, represents the miles per gallon obtained at a speed of x miles per hour. (a) Find the absolute maximum miles per gallon and the speed at which it occurs. (b) Find the absolute minimum miles per gallon and the speed at which it occurs. (a) The absolute maximum miles per gallon is . This occurs at mph. (Type integers or decimals rounded to the nearest thousandth as needed.) Find the absolute extrema if they exist, as well as all values of x where they occur, for the 1 1 function f(x) = 3x3 - 5x2 - 20x + 1 on the domain [- 5,6]. 1 3 1 2 Find the derivative of f(x) = 5x - Ex - 20x +1. f'(x)= x2 -x-20 Select the correct choice below and, if necessary, ll in the answer boxes to complete your choice. C) A- The absolute maximum is , which occurs at x = (Round the absolute maximum to tw0 decimal places as needed. Type an exact answer for the value of x where the maximum occurs. Use a comma to separate answers as needed.) C) B. There is no absolute maximum