5. After a new version of a certain type of computer is released, the total worldy profits (in billions of dollars) are approximated by the function 135t2 + 130t P(t) = t2+ 2t + 1 ° ,t >0 where t is measured in years after the computer's release. a) Find P'(t) using differentiation rules (by hand). b) Use Geogebra CAS to verify your answer in (a): · Define the function P(t) by inputting P(t) = if(t>=0, · Find the derivative of P(t) by inputting P' (t). c) How fast is the profit changing a year after the computer's release? d) What will the total profit be at that time? 13512+130t). e) What is lim P(t) and lim P'(t)? Explain what they mean in this situation.
5. After a new version of a certain type of computer is released, the total worldy profits (in billions of dollars) are approximated by the function 135t2 + 130t P(t) = t2+ 2t + 1 ° ,t >0 where t is measured in years after the computer's release. a) Find P'(t) using differentiation rules (by hand). b) Use Geogebra CAS to verify your answer in (a): · Define the function P(t) by inputting P(t) = if(t>=0, · Find the derivative of P(t) by inputting P' (t). c) How fast is the profit changing a year after the computer's release? d) What will the total profit be at that time? 13512+130t). e) What is lim P(t) and lim P'(t)? Explain what they mean in this situation.
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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Transcribed Image Text:5. After a new version of a certain type of computer is released, the total worldwide
profits (in billions of dollars) are approximated by the function
135t2 + 130t
P(t):
,t >0
t2 + 2t +1
where t is measured in years after the computer's release.
a) Find P'(t) using differentiation rules (by hand).
b) Use Geogebra CAS to verify your answer in (a):
· Define the function P(t) by inputting P(t) = if(t>=0, +1
135t2+130t
Uf).
Find the derivative of P(t) by inputting P' (t).
c) How fast is the profit changing a year after the computer's release?
d) What will the total profit be at that time?
e) What is lim P(t) and lim P'(t)? Explain what they mean in this situation.
t+00
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