In Exercises 7 − 12 , sketch the graph of a function that has the properties described. f ( − 1 ) = 0 ; f ' ( x ) < 0 for x < − 1 , f ' ( − 1 ) = 0 and f ' ( x ) > 0 for x > − 1 .
In Exercises 7 − 12 , sketch the graph of a function that has the properties described. f ( − 1 ) = 0 ; f ' ( x ) < 0 for x < − 1 , f ' ( − 1 ) = 0 and f ' ( x ) > 0 for x > − 1 .
As the speed of a train increases, the amount of power needed to maintain that speed increases, and the rate
of power increase also increases. Let P = f(v) be the power, in megawatts, needed for the train to maintain a
speed of v kilometers per hour.
(a) Sketch a possible graph of f.
(b) For each of the functions f, f', and f", decide whether the function is positive or negative, and explain
your answers.
(c) What requires a greater increase in power: increasing the train's speed from 100 to 150 kilometers per
hour, or increasing the train's speed from 200 to 250 kilometers per hour? Explain, based on your
answer to part (b).
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