Chapter 2: Q. 54 (page 184)
Use the definition of the derivative to find for each function in Exercises 39-54.
Short Answer
The derivative is
Chapter 2: Q. 54 (page 184)
Use the definition of the derivative to find for each function in Exercises 39-54.
The derivative 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?
Use the definition of the derivative to find the equations of the lines described in Exercises 59-64.
The tangent line to at
use the definition of derivative to directly prove the differentiation rules for constant and identity function
If 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 Katie’s position over time and a graph of Dave’s position over time on the same set of axes.
Taking the limit: We have seen that if f is a smooth function, then This approximation should get better as h gets closer to zero. In fact, in the next section we will define the derivative in terms of such a limit.
.
Use the limit just defined to calculate the exact slope of the tangent line toat
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