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If a stone is dropped from a height of 1,024 feet, its height s after t seconds is given by s(t) = 1,024 - 16t?, with s in feet. (a) Compute s'(t). Calculate -. Simplify your answer. s' (t) = y = (4x - 7)2 Find the stone's velocity at times t = 0, 1, 2, 3, and 4 seconds. ay = s'(0) = -16 ft/sec dy Vx - 7 s'(1) = ft/sec s'(2) ft/sec s'(3) : ft/sec s'(4)= ft/sec Calculate -. Simplify your answer. HINT [See Examples 1 and 2.] dx (b) When does the stone reach the ground, and how fast is it traveling when it hits the ground? HINT [It reaches the ground when s(t) = 0.] 3x - 5 The stone is traveling at a velocity of ft/sec when it hits the ground at seconds. y = _ 2x + 4 Find the marginal cost, marginal revenue, and marginal profit functions. dy 21 C(x) = 7x; R(x) = 9x - 0.001x2 dx 2(x+ 4)2 X marginal cost 7 Calculate -. You need not expand your answer. marginal revenue 9 dx X 001 y = x2 (2x + 5)(9x + 2) marginal profit X uy Find all values of x for which the marginal profit is zero. (Enter your answers as a comma-separated list.) x-(9x + 2) (2x + 5) X x = 0 Calculate - Y. You need not expand your answer. dx Find the marginal cost, marginal revenue, and marginal profit functions. C(x) = 4x2; R(x) = x3+ 5x+16 Vx - 9 marginal cost y = - Vx+ 9 marginal revenue dy marginal profit dx Find all values of x for which the marginal profit is zero. Interpret your answer. (Enter your answers as a comma-separated list.) X = Find the equation of the line tangent to the graph of the given function at the point with the indicated x-coordinate. f(x ) = (x0.5 + 4)(x2 + x); x = 1 A car wash firm calculates that its daily production (in number of cars washed) depends on the number n of workers it employs according to the formula y = p = 20n - 0.05n2 cars. Calculate the marginal product of labor at an employment level of 50 workers. HINT [See Example 3.] cars/worker Interpret the result. This means that, at an employment level of 50 workers, the firm's daily production will increase at a rate of cars per additional worker it hires