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A ball is thrown straight up with an initial velocity of 128 ft/sec, so that its height (in feet) after t sec is given by

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A ball is thrown straight up with an initial velocity of 128 ft/sec, so that its height (in feet) after t sec is given by s = f(t) = 128t - 16t2 . (a) What is the average velocity of the ball over the time interval [4, 4.1]? fu/sec (b) What is the instantaneous velocity at time t = 4? Use the definition of derivative to find the instantaneous velocity when t = 4. Show your work by completing the four-step process. (Simplify your answers completely for each step.) s = f(t) = 128t - 16t2 Step 1: f ( 4 + h) = Step 2: f ( 4 + h) - f(4) = (Hint: Factor completely.) Step 3: f( 4 + h) - f(4) = h Step 4: f ' (4) = lim (4 + h) - f(4) = --Select--- h-0 h

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