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Determine a, b, c and d so that the curve y = ax³ + bx² + cx+d₂ pass through (-1, -1) and have at (1, 3) an inflection point with inflectional tangent 4x - y = 1.

Determine a, b, c and d so that the curve y = ax³ + bx² + cx+d₂ pass through (-1, -1) and have at (1, 3) an inflection point with inflectional tangent 4x - y = 1.

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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differentials: critical points
please answer #8 #9 #10 with solutions thank you!

8. Determine a, b, c and d so that the curve y = ax³ + bx² + cx+d, pass through (-1, -1) and have at (1, 3) an inflection point with inflectional tangent 4x - y = 1. 9. Find a cubic function y = ax³ + bx² +cx+d that has a local maximum value of 3 at -2 and a local minimum value of 0 at 1. 10. Find a cubic function y = ax³ + bx² +cx+d that has a local maximum at (4, 0) and pass through (1, -1).
Transcribed Image Text:8. Determine a, b, c and d so that the curve y = ax³ + bx² + cx+d, pass through (-1, -1) and have at (1, 3) an inflection point with inflectional tangent 4x - y = 1. 9. Find a cubic function y = ax³ + bx² +cx+d that has a local maximum value of 3 at -2 and a local minimum value of 0 at 1. 10. Find a cubic function y = ax³ + bx² +cx+d that has a local maximum at (4, 0) and pass through (1, -1).
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