Chapter 2: Q. 24 (page 233)
Find the derivatives of each of the functions in Exercises 17–50. In some cases it may be convenient to do some preliminary algebra.
Short Answer
a
Chapter 2: Q. 24 (page 233)
Find the derivatives of each of the functions in Exercises 17–50. In some cases it may be convenient to do some preliminary algebra.
a
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Get started for freeLast 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?
Write down a rule for differentiating a composition of four functions
(a) in “prime” notation and
(b) in Leibniz notation.
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.
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:
When the bowling ball is first dropped, with
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.
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