Chapter 2: Q. 24 (page 233)
Find the derivatives of each of the functions in Exercises 17–50. In some cases it may be convenient to do some preliminary algebra.
Short Answer
a
Chapter 2: Q. 24 (page 233)
Find the derivatives of each of the functions in Exercises 17–50. In some cases it may be convenient to do some preliminary algebra.
a
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Get started for freeState the chain rule for differentiating a composition of two functions expressed
(a) in “prime” notation and
(b) in Leibniz notation.
Velocity is the derivative of position . It is also true that acceleration (the rate of change of velocity) is the derivative of velocity. If a race car’s position in miles t hours after the start of a race is given by the function , what are the units of ? What are the units and real-world interpretation of ? What are the units and real-world interpretations of ?
Find a function that has the given derivative and value. In each case you can find the answer with an educated guess and check process it may be helpful to do some preliminary algebra
Use the definition of the derivative to find for each function in Exercises 34-59
Suppose h(t) represents the average height, in feet, of a person who is t years old.
(a) In real-world terms, what does h(12) represent and what are its units? What does h' (12) represent, and what are its units?
(b) Is h(12) positive or negative, and why? Is h'(12) positive or negative, and why?
(c) At approximately what value of t would h(t) have a maximum, and why? At approximately what value of t would h' (t) have a maximum, and why?
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