Chapter 2: Q. 56 (page 222)
Use logarithmic differentiation to find the derivatives of each of the functions in Exercises 49–58.
The derivative of function is
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On earth, A falling object has a downward acceleration of 32 feet per second per second due to gravity. Suppose an object falls from an initial height of ,With an initial velocity of feet per second, Use antiderivatives to show that the equations for the position and velocity of the object after t seconds are respectively and
Use the definition of the derivative to find the equations of the lines described in Exercises 59-64.The line tangent to the graph of at the point
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.
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.
For each function and interval localid="1648297458718" in Exercises localid="1648297462718" , use the Intermediate Value Theorem to argue that the function must have at least one real root on localid="1648297466951" . Then apply Newton’s method to approximate that root.
localid="1648297471865"
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