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Chapter 2: Q. 60 (page 185)
Use the definition of the derivative to find the equations of the lines described in Exercises 59-64.
The tangent line to at
The equation of tangent is
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Use the definition of the derivative to find for each function in Exercises 39-54
Use (a) the definition of the derivative and then
(b) the definition of the derivative to find for each function f and value in Exercises 23–38.
27.
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.
Suppose h(t) represents the average height, in feet, of a person who is t years old.
(a) In real-world terms, what does h(12) represent and what are its units? What does h' (12) represent, and what are its units?
(b) Is h(12) positive or negative, and why? Is h'(12) positive or negative, and why?
(c) At approximately what value of t would h(t) have a maximum, and why? At approximately what value of t would h' (t) have a maximum, and why?
Suppose and . Use the chain rule to find role="math" localid="1648356625815" without first finding the formula for .
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