Chapter 2: Q 5. (page 237)
Translate expressions written in Leibniz notation to “prime” notation, and vice versa.
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Stuart left his house at noon and walked north on Pine Street for minutes. At that point he realized he was late for an appointment at the dentist, whose office was located south of Stuart’s house on Pine Street; fearing he would be late, Stuart sprinted south on Pine Street, past his house, and on to the dentist’s office. When he got there, he found the office closed for lunch; he was minutes early for his appointment. Stuart waited at the office for minutes and then found out that his appointment was actually for the next day, so he walked back to his house. Sketch a graph that describes Stuart’s position over time. Then sketch a graph that describes Stuart’s velocity over time.
For each function f that follows find all the x-values in the domain of f for which and all the values for which does not exist in later section we will call these values the critical points of f
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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
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.
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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