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.
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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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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