Chapter 2: Q. 34 (page 237)
Fill in the blanks to differentiate each of the given basic functions. You may assume that k, m, and b are appropriate constants:
Short Answer
The solution is
Chapter 2: Q. 34 (page 237)
Fill in the blanks to differentiate each of the given basic functions. You may assume that k, m, and b are appropriate constants:
The solution is
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Get started for freeUse the definition of the derivative to prove the following special case of the product rule
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?
Find the derivatives of the functions in Exercises 21โ46. Keep in mind that it may be convenient to do some preliminary algebra before differentiating.
Instead of choosing small values of h, we could have chosen values of z close to c. What limit involving z instead of h is equivalent to the one involving h?
For each function graphed in Exercises 65-68, determine the values of at which fails to be continuous and/or differentiable. At such points, determine any left or right continuity or differentiability. Sketch secant lines supporting your answers.
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