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 freeFind the derivatives of the functions in Exercises 21–46. Keep in mind that it may be convenient to do some preliminary algebra before differentiating.
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 that is perpendicular to the tangent line to at and also passes through the point
Use the definition of the derivative to find the equations of the lines described in Exercises 59-64.
The tangent line to at
Find a function that has the given derivative and value. In each case you can find the answer with an educated guess and check process it may be helpful to do some preliminary algebra
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