x²-2x+1 1. The function P (x) = models the proportion of a person's x2 -2x+4 social network that has received a particular piece of "news" (or more generally, information) x hours after the person first learned of it. Assume x > 0. a. Find and interpret the y-intercept in the context of this problem. In other words, explain in some detail what the y-intercept tells you in the context of this problem. b. When will half of the person's social network have received the piece of news? c. Use the first derivative to find intervals of inreasing / decreasing. d. Use the first derivative to find any local max/min. e. Use the second derivative to find intervals of concave up / down. f. Use the second derivative to find any points of inflection. Then interpret the points of inflection in the context of this problem. Be specific about what it measures.
x²-2x+1 1. The function P (x) = models the proportion of a person's x2 -2x+4 social network that has received a particular piece of "news" (or more generally, information) x hours after the person first learned of it. Assume x > 0. a. Find and interpret the y-intercept in the context of this problem. In other words, explain in some detail what the y-intercept tells you in the context of this problem. b. When will half of the person's social network have received the piece of news? c. Use the first derivative to find intervals of inreasing / decreasing. d. Use the first derivative to find any local max/min. e. Use the second derivative to find intervals of concave up / down. f. Use the second derivative to find any points of inflection. Then interpret the points of inflection in the context of this problem. Be specific about what it measures.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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
Transcribed Image Text:x²-2x+1
1. The function P (x)
models the proportion of a person's
x2 -2x+4
social network that has received a particular piece of "news" (or
more generally, information) x hours after the person first learned of
it. Assume x > 0.
a. Find and interpret the y-intercept in the context of this problem. In
other words, explain in some detail what the y-intercept tells you in the
context of this problem.
b. When will half of the person's social network have received the piece of
news?
c. Use the first derivative to find intervals of inreasing / decreasing.
d. Use the first derivative to find any local max/min.
e. Use the second derivative to find intervals of concave up / down.
f. Use the second derivative to find any points of inflection. Then interpret
the points of inflection in the context of this problem. Be specific about
what it measures.
g. Use a limit with L'Hospital's Rule to find any horiztonal asymptote.
Explain in words what a horizontal asymptote means in the context of this
problem.
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