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Suppose we have the points A = [0, 1], B = [1, 3], C = [2, 2] and D= [3,2] (you may have to move D in the GeoGebra app). These points are joined by the functions p(x) = 1 + 2x + x² – x³ (blue) on the interval [0, 1] = 5x – 2x² (red) on the interval [1, 2] and r(x) = ax³ + bx² + cx + d (black) on the interval [2, 3]. q(x)

Suppose we have the points A = [0, 1], B = [1, 3], C = [2, 2] and D= [3,2] (you may have to move D in the GeoGebra app). These points are joined by the functions p(x) = 1 + 2x + x² – x³ (blue) on the interval [0, 1] = 5x – 2x² (red) on the interval [1, 2] and r(x) = ax³ + bx² + cx + d (black) on the interval [2, 3]. q(x)

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter4: Polynomial And Rational Functions
Section: Chapter Questions
Problem 15RE
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A B (2 -1 0 2 3 4 = [3,2] (you may have to move D in the Suppose we have the points A = [0, 1], B = [1, 3], C = [2, 2] and D = GeoGebra app). These points are joined by the functions p(x) = 1 + 2x + x² - x³ (blue) on the interval [0, 1] q(x) = 5x – 2x² (red) on the interval [1, 2] and r(x) = ax³ + bx² + cx+d (black) on the interval [2, 3]. The cubic polynomials p and q: 1. meet at the point B 2. share the same first derivative at B, namely p' (1) = q' (1) = 1 3. share the same second derivative at B, namely p" (1) = q" (1) : = -4 Now we can find try to find the cubic polynomial r(x) which passes through C and D and agrees with g(x) at Cup to its second derivative. Can you find r(x) = BD? Note: Don't forget that you might need to move D in the GeoGebra app.
Transcribed Image Text:A B (2 -1 0 2 3 4 = [3,2] (you may have to move D in the Suppose we have the points A = [0, 1], B = [1, 3], C = [2, 2] and D = GeoGebra app). These points are joined by the functions p(x) = 1 + 2x + x² - x³ (blue) on the interval [0, 1] q(x) = 5x – 2x² (red) on the interval [1, 2] and r(x) = ax³ + bx² + cx+d (black) on the interval [2, 3]. The cubic polynomials p and q: 1. meet at the point B 2. share the same first derivative at B, namely p' (1) = q' (1) = 1 3. share the same second derivative at B, namely p" (1) = q" (1) : = -4 Now we can find try to find the cubic polynomial r(x) which passes through C and D and agrees with g(x) at Cup to its second derivative. Can you find r(x) = BD? Note: Don't forget that you might need to move D in the GeoGebra app.
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