Chapter 2: Q. 18 (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.
Chapter 2: Q. 18 (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.
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Get started for freeStuart 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.
Use the definition of the derivative to find the equations of the lines described in Exercises 59-64.
The tangent line to at
Use the definition of the derivative to find for each function in Exercises 34-59
For each function and interval in Exercises , use the Intermediate Value Theorem to argue that the function must have at least one real root on . Then apply Newton’s method to approximate that root.
use the definition of derivative to directly prove the differentiation rules for constant and identity function
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