(i) If a data set has nturning points where n∈W, and you wish to model the data with a polynomial, what is the least possible degree of that polynomial? Explain. (ii) Consider the following data set: {(0,0),(1,−3),(2,0),(−1,3)}.Draw a scat- ter plot of this data set. Based only off the scatter plot, what degree polynomial would you suggest? (iii) Show that each point in the relation for (ii) satisfies the equation y= x(x−2)(x+ 2). (iv) Show that there is no function y= ax2 + bx+ cwhich satisfies all 4 data points in (ii). In light of (iii) and (iv), reconsider your answer to (ii).
(i) If a data set has nturning points where n∈W, and you wish to model the data with a polynomial, what is the least possible degree of that polynomial? Explain. (ii) Consider the following data set: {(0,0),(1,−3),(2,0),(−1,3)}.Draw a scat- ter plot of this data set. Based only off the scatter plot, what degree polynomial would you suggest? (iii) Show that each point in the relation for (ii) satisfies the equation y= x(x−2)(x+ 2). (iv) Show that there is no function y= ax2 + bx+ cwhich satisfies all 4 data points in (ii). In light of (iii) and (iv), reconsider your answer to (ii).
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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Question
1)
(i) If a data set has nturning points where n∈W, and you wish to model
the data with a polynomial, what is the least possible degree of that polynomial?
Explain.
(ii) Consider the following data set: {(0,0),(1,−3),(2,0),(−1,3)}.Draw a scat-
ter plot of this data set. Based only off the
would you suggest?
(iii) Show that each point in the relation for (ii) satisfies the equation y=
x(x−2)(x+ 2).
(iv) Show that there is no function y= ax2 + bx+ cwhich satisfies all 4 data
points in (ii). In light of (iii) and (iv), reconsider your answer to (ii).
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