Chapter 2: Q. 88 (page 235)
Use implicit differentiation and the fact that for all in the domain of to prove that . You will have to consider the casesand separately.
Short Answer
We proved usingimplicit differentiation.
Chapter 2: Q. 88 (page 235)
Use implicit differentiation and the fact that for all in the domain of to prove that . You will have to consider the casesand separately.
We proved usingimplicit differentiation.
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Get started for freeVelocity is the derivative of position . It is also true that acceleration (the rate of change of velocity) is the derivative of velocity. If a race car’s position in miles t hours after the start of a race is given by the function , what are the units of ? What are the units and real-world interpretation of ? What are the units and real-world interpretations of ?
Use the definition of the derivative to find for each function in Exercises39-54
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.
Prove the difference rule in two ways
a) using definition of the derivative
b) using sum and constant multiple rules
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?
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