Chapter 3 | Derivatives
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48. [T] The total cost C ( x ), in hundreds of dollars, to produce x jars of mayonnaise is given by C ( x ) = 0.000003 x 3 +4 x +300. a. Calculate the average cost per jar over the following intervals: i. [100, 100.1] ii. [100, 100.01] iii. [100, 100.001] iv. [100, 100.0001] b. Use the answers from a. to estimate the average cost to produce 100 jars of mayonnaise. 49. [T] For the function f ( x ) = x 3 −2 x 2 −11 x +12, do the following. a. Use a graphing calculator to graph f in an appropriate viewing window. b. Use the ZOOM feature on the calculator to approximate the two values of x = a for which m tan = f ′( a ) =0. 50. [T] For the function f ( x ) = x 1+ x 2 , do the following. a. Use a graphing calculator to graph f in an appropriate viewing window. b. Use the ZOOM feature on the calculator to approximate the values of x = a for which m tan = f ′( a ) =0. 51. Suppose that N ( x ) computes the number of gallons of gas used by a vehicle traveling x miles. Suppose the vehicle gets 30 mpg. a. Find a mathematical expression for N ( x ). b. What is N (100)? Explain the physical meaning. c. What is N ′(100)? Explain the physical meaning. 52. [T] For the function f ( x ) = x 4 −5 x 2 +4, do the following. a. Use a graphing calculator to graph f in an appropriate viewing window. b. Use the nDeriv function, which numerically finds the derivative, on a graphing calculator to estimate f ′(−2), f ′(−0.5), f ′(1.7), and f ′(2.718). 53. [T] For the function f ( x ) = x 2 x 2 +1 , do the following. a. Use a graphing calculator to graph f in an appropriate viewing window. b. Use the nDeriv function on a graphing calculator to find f ′(−4), f ′(−2), f ′(2), and f ′(4).
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