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Consider the function Q R RH n the region z>0, where P, Q and R are all positive constants. (a) Find an inequality satisfied by P, Q and R in order for f(x) to have at least one real root. (b) Find a relationship between P, Q and R in order for f(x) to have exactly one stationary point. (c) If the relationshiop of the previous part holds, so that exactly one stationary point exists, what is the nature of that stationary point and at what value of r (expressed in terms of P, Q and R) is it? It is not necessary to work out a second derivative to answer this.

Consider the function Q R RH n the region z>0, where P, Q and R are all positive constants. (a) Find an inequality satisfied by P, Q and R in order for f(x) to have at least one real root. (b) Find a relationship between P, Q and R in order for f(x) to have exactly one stationary point. (c) If the relationshiop of the previous part holds, so that exactly one stationary point exists, what is the nature of that stationary point and at what value of r (expressed in terms of P, Q and R) is it? It is not necessary to work out a second derivative to answer this.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Consider the function Q R RH n the region z>0, where P, Q and R are all positive constants. (a) Find an inequality satisfied by P, Q and R in order for f(x) to have at least one real root. (b) Find a relationship between P, Q and R in order for f(x) to have exactly one stationary point. (c) If the relationshiop of the previous part holds, so that exactly one stationary point exists, what is the nature of that stationary point and at what value of r (expressed in terms of P, Q and R) is it? It is not necessary to work out a second derivative to answer this.
Transcribed Image Text:Consider the function Q R RH n the region z>0, where P, Q and R are all positive constants. (a) Find an inequality satisfied by P, Q and R in order for f(x) to have at least one real root. (b) Find a relationship between P, Q and R in order for f(x) to have exactly one stationary point. (c) If the relationshiop of the previous part holds, so that exactly one stationary point exists, what is the nature of that stationary point and at what value of r (expressed in terms of P, Q and R) is it? It is not necessary to work out a second derivative to answer this.
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