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Calculus 5e_Part153 - 304 CHAPTER 4 APPLICATIONS OF...

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304 ❙❙❙❙ CHAPTER 4 APPLICATIONS OF DIFFERENTIATION The graph of the second derivative of a function is shown. State the -coordinates of the in fl ection points of . Give rea- sons for your answers. 8. The graph of the fi rst derivative of a function is shown. (a) On what intervals is increasing? Explain. (b) At what values of does have a local maximum or mini- mum? Explain. (c) On what intervals is concave upward or concave down- ward? Explain. (d) What are the -coordinates of the in fl ection points of ? Why? 9. Sketch the graph of a function whose fi rst and second deriva- tives are always negative. 10. A graph of a population of yeast cells in a new laboratory cul- ture as a function of time is shown. (a) Describe how the rate of population increase varies. (b) When is this rate highest? (c) On what intervals is the population function concave upward or downward? (d) Estimate the coordinates of the in fl ection point. 11–20 |||| (a) Find the intervals on which is increasing or decreasing. (b) Find the local maximum and minimum values of . (c) Find the intervals of concavity and the in fl ection points. 11. 12. f x 5 3 x 2 x 3 f x x 3 12 x 1 f f 2 0 Time (in hours) 6 10 14 Number of yeast cells 4 8 12 16 18 100 200 300 400 500 600 700 3 y 0 x 5 7 1 9 y=fª(x) f x f f x f f f y=f·(x) 2 y 0 x 4 6 8 1 f x f f 7.
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