1. Let b, c, d be real numbers, and let a be a nonzero real number. Consider the function f: R → R defined by f(x) = ax³ + bx² + cx + d, and consider the function g: R→ R defined by g(x) = x³ - 6x² + 9x +7. A. The equation f"(x) = 0 will always have exactly one solution, and if that solution is called to, then the point (xo, f(xo)) must be an inflection point of function f. Explain. B. Find the critical points of function g. C. Use the first derivative test to classify the critical points of g. D. Use the second derivative test to classify the critical points of function g, and find the inflection point of function g.
1. Let b, c, d be real numbers, and let a be a nonzero real number. Consider the function f: R → R defined by f(x) = ax³ + bx² + cx + d, and consider the function g: R→ R defined by g(x) = x³ - 6x² + 9x +7. A. The equation f"(x) = 0 will always have exactly one solution, and if that solution is called to, then the point (xo, f(xo)) must be an inflection point of function f. Explain. B. Find the critical points of function g. C. Use the first derivative test to classify the critical points of g. D. Use the second derivative test to classify the critical points of function g, and find the inflection point of function g.
Big Ideas Math A Bridge To Success Algebra 1: Student Edition 2015
1st Edition
ISBN:9781680331141
Author:HOUGHTON MIFFLIN HARCOURT
Publisher:HOUGHTON MIFFLIN HARCOURT
Chapter9: Solving Quadratic Functions
Section: Chapter Questions
Problem 1CA
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a, b, c, and d.
Transcribed Image Text:1. Let b, c, d be real numbers, and let a be a nonzero real number. Consider the function f: R → R defined by f(x) = ax³ + bx² + cx + d, and
consider the function g: R → R defined by g(x) = x³ 6x² +9x +7.
A. The equation f" (x) = 0 will always have exactly one solution, and if that solution is called o, then the point (xo, f(x)) must be an inflection
point of function f. Explain.
B. Find the critical points of function g.
C. Use the first derivative test to classify the critical points of g.
D. Use the second derivative test to classify the critical points of function g, and find the inflection point of function g.
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