Chapter 2: Q. 30 (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
The derivative of the given function is: 1.
Chapter 2: Q. 30 (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.
The derivative of the given function is: 1.
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Get started for freeFor each function f and value in Exercises 35–44, use a sequence of approximations to estimate . Illustrate your work with an appropriate sequence of graphs of secant lines.
Taking the limit: We have seen that if f is a smooth function, then This approximation should get better as h gets closer to zero. In fact, in the next section we will define the derivative in terms of such a limit.
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Use the limit just defined to calculate the exact slope of the tangent line toat
A tomato plant given ounces of fertilizer will successfully bear pounds of tomatoes in a growing season.
(a) In real-world terms, what does represent and what are its units? What does represent and what are its units?
(b) A study has shown that this fertilizer encourages tomato production when less than ounces are used, but inhibits production when more than ounces are used. When is positive and when is negative? When is positive and when is negative?
Use the definition of the derivative to find for each function in Exercises 34-59
Find the derivatives of the functions in Exercises 21–46. Keep in mind that it may be convenient to do some preliminary algebra before differentiating.
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