Suppose that a polynomial function y = f(x) has local approximations at its x-intercepts given by: i. The local approximation at x = 0, is given by y = -2x? ii. The local approximation at x = 3, is given by y = -(x – 3)² iii. The local approximation at x = 6, is given by y = -4x³ a) Sketch the graph of a polynomial, having the lowest degree, that displays these three constraints b) Determine the y-intercept of the polynomial function c) Is the polynomial of even degree or is of odd degree? Explain why.
Suppose that a polynomial function y = f(x) has local approximations at its x-intercepts given by: i. The local approximation at x = 0, is given by y = -2x? ii. The local approximation at x = 3, is given by y = -(x – 3)² iii. The local approximation at x = 6, is given by y = -4x³ a) Sketch the graph of a polynomial, having the lowest degree, that displays these three constraints b) Determine the y-intercept of the polynomial function c) Is the polynomial of even degree or is of odd degree? Explain why.
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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Transcribed Image Text:Suppose that a polynomial function y = f(x) has local approximations at its x-intercepts given
by:
i.
The local approximation at x = 0, is given by y = –2x²
ii.
The local approximation at x = 3, is given by y = -(x – 3)²
iii.
The local approximation at x = 6, is given by y = –4x³
a) Sketch the graph of a polynomial, having the lowest degree, that displays these three
constraints
b) Determine the y-intercept of the polynomial function
c) Is the polynomial of even degree or is of odd degree? Explain why.
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