Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN: 9781285741550
Author: James Stewart
Publisher: Cengage Learning
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As a result of increasing energy costs, the growth rate of the profit of a 4-year old glassblowing company has begun to decline. The company's
management, after consulting with energy experts, decides to implement certain energy-conservation measures aimed at cutting energy bills.
The general manager reports that, according to his calculations, the growth rate of their profit should be on the increase again within 5 years. If
the glassblowing company's profit (in hundreds of dollars) t years from now is given by the function
P(t) = t - 16t? + 25t + 50
(0 <t< 8)
%3D
determine whether the general manager's forecast will be accurate.
Hint: Find the inflection point of the function P and study the concavity of P.
Yes, the forecast will be accurate.
No, the forecast will not be accurate.
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Transcribed Image Text:As a result of increasing energy costs, the growth rate of the profit of a 4-year old glassblowing company has begun to decline. The company's management, after consulting with energy experts, decides to implement certain energy-conservation measures aimed at cutting energy bills. The general manager reports that, according to his calculations, the growth rate of their profit should be on the increase again within 5 years. If the glassblowing company's profit (in hundreds of dollars) t years from now is given by the function P(t) = t - 16t? + 25t + 50 (0 <t< 8) %3D determine whether the general manager's forecast will be accurate. Hint: Find the inflection point of the function P and study the concavity of P. Yes, the forecast will be accurate. No, the forecast will not be accurate.
Expert Solution
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Step 1

Here P(t)=t3-16t2+25t+50         , (0t8)

The inflection point is the point where F''(t)=0

Then at that point we will find P(t) at t=that value where F''(t)=0.

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