Chapter 2: Q. 61 (page 185)
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
Short Answer
The equation of tangent line is
Chapter 2: Q. 61 (page 185)
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
The equation of tangent line is
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Get started for freeIf Katie walked at miles per hour for minutes and then sprinted at miles an hour for minutes, how fast would Dave have to walk or run to go the same distance as Katie did at the same time while moving at a constant speed? Sketch a graph of Katieโs position over time and a graph of Daveโs position over time on the same set of axes.
Use (a) the definition of the derivative and then
(b) the definition of the derivative to find for each function f and value in Exercises 23โ38.
24.
Find the derivatives of the functions in Exercises 21โ46. Keep in mind that it may be convenient to do some preliminary algebra before differentiating.
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
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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