Chapter 2: Q. 85 (page 211)
Chapter 2: Q. 85 (page 211)
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Get started for freeProve that if f is any cubic polynomial function then the coefficients of f are completely determined by the values of f(x) and its derivative at x=0 as follows
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"
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 thedefinition of the derivative to prove the power rule holds for positive integers powers
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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