1. The cost of running an assembly line can be modeled by the function, C(x)=0.3x -0.9x+1.675,...

  

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1. The cost of running an assembly line can be modeled by the function, C(x)=0.3x -0.9x+1.675, where C(x) is the cost per hour in thousands of dollars and x is the number of items produced per hour in thousands. The most economical production level occurs when 1500 items are produced. Verify this using the appropriate calculations for rate of change in cost. 2. For each function, the point given is the maximum or minimum. Use the difference quotient to verify that the slope of the tangent at this point is zero. a) f(x)=0.5x +6x+7.5 ; f(-6)=-10.5 b) 3. Use an algebraic strategy to verify that the point given for each function is either a maximum or a minimum. a) f(x)=5sinx ; (-)-5 = 2 b) f(x)=x-4x+5; (2,1) f(x)=-x +12x-1; (2,15) 3 1. Consider the graph showing a bicyclist's elevation relative to his elevation above sea level at the start of the race. The first 20 s of the race are shown. a) h 8- LA 4- 4 8 12 16 20 Time (s) Height (m) a) b) b) 2. A construction worker drops a bolt while working on a high-rise building 320 m above the ground. After t seconds, the bolt's height above the ground is s meters, where s(t) = 320-5t, 0t8. On which intervals will the tangent slope be positive? Negative? Zero? What do these slopes tell you about the elevation of the bicyclist? 600 Find the average velocity for the interval 3t8. Find the bolt's velocity at t = 2 s. 3. The height, h, in meters of a toy rocket above the ground can be modeled by the function h(t) = -5t +50t, where t represent time in seconds. Find the instantaneous speed at t = 4 s. Find the instantaneous speed at t = 10 s. What is the average speed over the interval from t=0 to t= 10? 1. The cost of running an assembly line can be modeled by the function, C(x)=0.3x -0.9x+1.675, where C(x) is the cost per hour in thousands of dollars and x is the number of items produced per hour in thousands. The most economical production level occurs when 1500 items are produced. Verify this using the appropriate calculations for rate of change in cost. 2. For each function, the point given is the maximum or minimum. Use the difference quotient to verify that the slope of the tangent at this point is zero. a) f(x)=0.5x +6x+7.5 ; f(-6)=-10.5 b) 3. Use an algebraic strategy to verify that the point given for each function is either a maximum or a minimum. a) f(x)=5sinx ; (-)-5 = 2 b) f(x)=x-4x+5; (2,1) f(x)=-x +12x-1; (2,15) 3 1. Consider the graph showing a bicyclist's elevation relative to his elevation above sea level at the start of the race. The first 20 s of the race are shown. a) h 8- LA 4- 4 8 12 16 20 Time (s) Height (m) a) b) b) 2. A construction worker drops a bolt while working on a high-rise building 320 m above the ground. After t seconds, the bolt's height above the ground is s meters, where s(t) = 320-5t, 0t8. On which intervals will the tangent slope be positive? Negative? Zero? What do these slopes tell you about the elevation of the bicyclist? 600 Find the average velocity for the interval 3t8. Find the bolt's velocity at t = 2 s. 3. The height, h, in meters of a toy rocket above the ground can be modeled by the function h(t) = -5t +50t, where t represent time in seconds. Find the instantaneous speed at t = 4 s. Find the instantaneous speed at t = 10 s. What is the average speed over the interval from t=0 to t= 10?