Chapter 2: Q. 67 (page 198)
Find the derivatives of each of the absolute value and piecewise-defined functions in Exercises 65-72.
Short Answer
The derivative of the function is.
Chapter 2: Q. 67 (page 198)
Find the derivatives of each of the absolute value and piecewise-defined functions in Exercises 65-72.
The derivative of the function is.
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Get started for freeA tomato plant given ounces of fertilizer will successfully bear pounds of tomatoes in a growing season.
(a) In real-world terms, what does represent and what are its units? What does represent and what are its units?
(b) A study has shown that this fertilizer encourages tomato production when less than ounces are used, but inhibits production when more than ounces are used. When is positive and when is negative? When is positive and when is negative?
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.
Each graph in Exercises 31–34 can be thought of as the associated slope function f' for some unknown function f. In each case sketch a possible graph of f.
For each function and interval in Exercises , use the Intermediate Value Theorem to argue that the function must have at least one real root on . Then apply Newton’s method to approximate that root.
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
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