Chapter 2: Q. 55 (page 210)
Suppose that r is an independent variable, s is a function of r, and q is a constant. Calculate the derivatives in Exercises 53– 58. Your answers may involve r, s, q, or their derivatives.
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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
Last night Phil went jogging along Main Street. His distance from the post office t minutes after p.m. is shown in the preceding graph at the right.
(a) Give a narrative (that matches the graph) of what Phil did on his jog.
(b) Sketch a graph that represents Phil’s instantaneous velocity t minutes after p.m. Make sure you label the tick marks on the vertical axis as accurately as you can.
(c) When was Phil jogging the fastest? The slowest? When was he the farthest away from the post office? The closest to the post office?
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.
Use the definition of the derivative to find for each function in Exercises 34-59
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State the chain rule for differentiating a composition of two functions expressed
(a) in “prime” notation and
(b) in Leibniz notation.
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