Explain how to graph the derivative of a function given

Problem 24A Weight Gain The graph below shows the typical weight (in kilograms) of an English boy for his first 18 years of life. Sketch the graph of the rate of change of weight with respect to time. Source: Human Growth After Birth.

Problem 2E Explain how to graph a function given the graph of the derivative function. Note that the answer is not unique.

Problem 3E The graphing calculator window shows the graph of a function f(x) and its derivative function f?(x). Decide which is the graph of the function and which is the graph of the derivative.

Problem 1E Explain how to graph the derivative of a function given the graph of the function.

Problem 4E The graphing calculator window shows the graph of a function f(x) and its derivative function f?(x). Decide which is the graph of the function and which is the graph of the derivative.

Problem 5E The graphing calculator window shows the graph of a function f(x) and its derivative function f?(x). Decide which is the graph of the function and which is the graph of the derivative.

Problem 6E The graphing calculator window shows the graph of a function f(x) and its derivative function f?(x). Decide which is the graph of the function and which is the graph of the derivative.

Problem 7E Sketch the graph of the derivative for each function shown.

Problem 8E Sketch the graph of the derivative for each function shown.

Problem 9E Sketch the graph of the derivative for each function shown.

Problem 10E Sketch the graph of the derivative for each function shown.

Problem 11E Sketch the graph of the derivative for each function shown.

Problem 12E Sketch the graph of the derivative for each function shown.

Problem 13E Sketch the graph of the derivative for each function shown.

Problem 14E Sketch the graph of the derivative for each function shown.

Problem 15E Sketch the graph of the derivative for each function shown.

Problem 16E Sketch the graph of the derivative for each function shown.

Problem 17A Consumer Demand When the price of an essential commodity rises rapidly, consumption drops slowly at first. If the price continues to rise, however, a “tipping” point may be reached, at which consumption takes a sudden substantial drop. Suppose the accompanying graph shows the consumption of gasoline, G(t), in millions of gallons, in a certain area. We assume that the price is rising rapidly. Here t is the time in months after the price began rising. Sketch a graph of the rate of change in consumption as a function of time.

Problem 18A Sales The graph shows annual sales (in thousands of dollars) of a Nintendo game at a particular store. Sketch a graph of the rate of change of sales as a function of time.

Problem 19A Insecticide The graph in the next column shows how the number of arthropod species resistant to insecticides has varied with time. Sketch a graph of the rate of change of the insecticide-resistant species as a function of time. Source: Science.

Problem 23A Human Growth The growth remaining in sitting height at consecutive skeletal age levels is indicated below for boys. Source: Standards in Pediatric Orthopedics: Tables, Charts, and Graphs Illustrating Growth. Sketch a graph showing the rate of change of growth remaining for the indicated years. Use the graph and your sketch to estimate the remaining growth and the rate of change of remaining growth for a 14-year-old boy.

Problem 22A Flight Speed The graph on the next page shows the relationship between the speed of a bird in flight and the required power expended by flight muscles. Sketch the graph of the rate of change of the power as a function of the speed. Source: Biolog-e: The Undergraduate Bioscience Research Journal.

Problem 20A Body Mass Index The following graph shows how the body mass index-for-age percentile for boys varies from the age of 2 to 20 years. Source: Centers for Disease Control. a. Sketch a graph of the rate of change of the 95th percentile as a function of age. ________________ b. Sketch a graph of the rate of change of the 50th percentile as a function of age.

Problem 21A Shellfish Population In one research study, the population of a certain shellfish in an area at time t was closely approximated by the following graph. Sketch a graph of the growth rate of the population.