Chapter 2: Q. 49 (page 184)
Use the definition of the derivative to find for each function in Exercises 34-59
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Short Answer
The value of
Chapter 2: Q. 49 (page 184)
Use the definition of the derivative to find for each function in Exercises 34-59
role="math" localid="1648284617718"
The value of
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Get started for freeuse the definition of derivative to directly prove the differentiation rules for constant and identity function
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.
Use the definition of the derivative to find the equations of the lines described in Exercises 59-64.
The tangent line to at
Think about what you did today and how far north you were from your house or dorm throughout the day. Sketch a graph that represents your distance north from your house or dorm over the course of the day, and explain how the graph reflects what you did today. Then sketch a graph of your velocity.
Last night Phil went jogging along Main Street. His distance from the post office t minutes after p.m. is shown in the preceding graph at the right.
(a) Give a narrative (that matches the graph) of what Phil did on his jog.
(b) Sketch a graph that represents Phil’s instantaneous velocity t minutes after p.m. Make sure you label the tick marks on the vertical axis as accurately as you can.
(c) When was Phil jogging the fastest? The slowest? When was he the farthest away from the post office? The closest to the post office?
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