Chapter 2: Q3 (page 197)
Express the constant multiple, sum, and difference rules in Leibniz/operator notation
Chapter 2: Q3 (page 197)
Express the constant multiple, sum, and difference rules in Leibniz/operator notation
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Get started for freeFor each function f that follows find all the x-values in the domain of f for which and all the values for which does not exist in later section we will call these values the critical points of f
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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 Philโs 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?
Suppose h(t) represents the average height, in feet, of a person who is t years old.
(a) In real-world terms, what does h(12) represent and what are its units? What does h' (12) represent, and what are its units?
(b) Is h(12) positive or negative, and why? Is h'(12) positive or negative, and why?
(c) At approximately what value of t would h(t) have a maximum, and why? At approximately what value of t would h' (t) have a maximum, and why?
Use the definition of the derivative to find the equations of the lines described in Exercises 59-64.
The line tangent to the graph of at the point
use the definition of derivative to directly prove the differentiation rules for constant and identity function
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