Chapter 4.3, Problem 41E

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).

ents B Mobius - MAT-136-H3725 Intro 1 X m Southern New Hampshire Univer X modules/unproctored Test.QuestionSheet Answer the vertical line test questions below. a. Use the vertical line test to determine if the relation shown in the graph below is a function. Yes, it is a function. ONo. it is not a function. Submit Assignment Quit & Save Back Question Menu - 1:11 44°F al 1/23 ■ 童 0

Explain how the real-world meaning of a derivative is related to the independent (input) and dependent (output) variables of the problem. Use your explanation in a real-world contextual situation of your choosing. Also, include a sketch of the two axes (independent and dependent) that you use to help clarify your discussion for the reader. Please explain and sketch a graph of two axes.

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How do some functions vary continuously?

A table for the function (x) is shown to the right. Use the table to answer the questions below. y = fx) 84 21 70 (a) f(42) = Number 42 63 (b) f- (21) = Number 63 49 70 42 (c) ƒ ( Number ) = 70 84 21 (d) f-' ( Number ) = 70

In Exercises 43 and 44, find all derivatives of the function. 3 44. y = 120 43. y = 2

determine a function by being given the function’s first derivative and an initial condition for the function. Discuss how you would determine an original function if you were given the second derivative of the function as well initial conditions on the first derivative and original function.

I don't understand this at all please help