Since the start of July, OHaganBooks.com has seen its weekly sales increase. OHaganBooks.com fits the curve w(t) = 36t2 + 245t + 6,238  (0 ≤ t ≤ 6) to its weekly sales figures as shown in the following graph. The t w coordinate plane is given with horizontal axis labeled "weeks" and vertical axis labeled "book sales." Six points are plotted with a curve through them. The curve enters the window at approximately w = 6240 on the positive w-axis, goes up and right becoming more steep, and exits the window in the first quadrant. (a) Compute the derivative function w′(t). w′(t) =

Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Since the start of July, OHaganBooks.com has seen its weekly sales increase.
OHaganBooks.com fits the curve
w(t) = 36t2 + 245t + 6,238  (0 ≤ t ≤ 6)
to its weekly sales figures as shown in the following graph.
The t w coordinate plane is given with horizontal axis labeled "weeks" and vertical axis labeled "book sales." Six points are plotted with a curve through them. The curve enters the window at approximately w = 6240 on the positive w-axis, goes up and right becoming more steep, and exits the window in the first quadrant.
(a)
Compute the derivative function w′(t).
w′(t) =
 
 
(b)
According to the model, what was the rate of increase of sales at the beginning of the second week (t = 1)?
books per week
(c)
If we extrapolate the model, what would be the rate of increase of weekly sales at the beginning of the eighth week (t = 7)?
books per week
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