Chapter 2: Q 25. (page 237)
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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.
Differentiation review: Without using the chain rule find the derivative of each of the function f that follows some algebra may be required before differentiating
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.
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Use the limit just defined to calculate the exact slope of the tangent line toat
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
Prove the difference rule in two ways
a) using definition of the derivative
b) using sum and constant multiple rules
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