Chapter 2: Q. 48 (page 222)
Describe the derivatives of each of the piecewise-defined functions in Exercises 45–48.
Short Answer
The derivative of function is
Chapter 2: Q. 48 (page 222)
Describe the derivatives of each of the piecewise-defined functions in Exercises 45–48.
The derivative of function is
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Get started for freeUse 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 the derivative to find for each function in Exercises
Find the derivatives of the functions in Exercises 21–46. Keep in mind that it may be convenient to do some preliminary algebra before differentiating.
Use thedefinition of the derivative to prove the power rule holds for positive integers powers
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?
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