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Chapter 2: Q 33. (page 222)
Find the derivatives of the functions:
The required answer is.
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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鈥檚 method to approximate that root.
Use the limit you just found to calculate the exact slope of the tangent line to at . Obviously you should get the same final answer as you did earlier.
Use the definition of the derivative to prove the following special case of the product rule
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鈥檚 position over time and a graph of Dave鈥檚 position over time on the same set of axes.
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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