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Chapter 2: Q 2 (a). (page 237)
Fill in the blanks to complete each of the following theorem statements:
If a function is differentiable at , then is at ---------.
continuous
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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?
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
Use the definition of the derivative to find for each function in Exercises
Use the differentiation rules developed in this section to find
the derivatives of the functions
Each graph in Exercises 31–34 can be thought of as the associated slope function f' for some unknown function f. In each case sketch a possible graph of f.
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