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Chapter 2: Q. 69 (page 223)
Use the chain rule to prove that
The given function has been proved.
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A bowling ball dropped from a height of feet will be feet from the ground after seconds. Use a sequence of average velocities to estimate the instantaneous velocities described below:
After seconds, with
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?
The following reciprocal rules tells us hoe to differentiate the reciprocal of a function
Prove this using
a) definition of the derivative
b) by using the quotient rule
Find the derivatives of the functions in Exercises 21鈥�46. Keep in mind that it may be convenient to do some preliminary algebra before differentiating.
Use the limit you just found to calculate the exact slope of the tangent line to at . Obviously you should get the same final answer as you did earlier.
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