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Let f be a function with f(x) > 0 for all x. Let g = 1/f. (a) If f is increasing in an interval around xo, what about g? O We cannot tell whether g is increasing or decreasing in an interval around xo O g is decreasing in an interval around xo. g is zero in an interval around xo. g is constant in an interval around xo. O g is increasing in an interval around xo. (b) If f has a local maximum at x₁, what about g? Og has a local maximum at X₁. g has an inflection point at x₁. g has both a local minimum and a local maximum at X₁. We cannot tell whether g has a local minimum or a local maximum at x₁. Og has a local minimum at X₁. (c) If f is concave down at x2, what about g? O We cannot tell whether g is concave up or concave down at X₂. g is flat at x₂. g is concave up at x₂. Og is concave down at x2. O g is increasing at X2.

Let f be a function with f(x) > 0 for all x. Let g = 1/f. (a) If f is increasing in an interval around xo, what about g? O We cannot tell whether g is increasing or decreasing in an interval around xo O g is decreasing in an interval around xo. g is zero in an interval around xo. g is constant in an interval around xo. O g is increasing in an interval around xo. (b) If f has a local maximum at x₁, what about g? Og has a local maximum at X₁. g has an inflection point at x₁. g has both a local minimum and a local maximum at X₁. We cannot tell whether g has a local minimum or a local maximum at x₁. Og has a local minimum at X₁. (c) If f is concave down at x2, what about g? O We cannot tell whether g is concave up or concave down at X₂. g is flat at x₂. g is concave up at x₂. Og is concave down at x2. O g is increasing at X2.

Calculus: Early Transcendentals
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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Let f be a function with f(x) > 0 for all x . Let g = 1/f. (a) If f is increasing in an interval around xo, what about g? O We cannot tell whether g is increasing or decreasing in an interval around xo. g is decreasing in an interval around xo. g is zero in an interval around xo. O g is constant in an interval around xo. g is increasing in an interval around xo. (b) If f has a local maximum at x₁, what about g? g has a local maximum at x1. g has an inflection point at X₁. g has both a local minimum and a local maximum at x₁. We cannot tell whether g has a local minimum or a local maximum at x₁. Og has a local minimum at X₁. (c) If f is concave down at x2, what about g? O We cannot tell whether g is concave up or concave down at X2. Og is flat at X2. Og is concave up at X₂. O g is concave down at x₂. g is increasing at X2.
Transcribed Image Text:Let f be a function with f(x) > 0 for all x . Let g = 1/f. (a) If f is increasing in an interval around xo, what about g? O We cannot tell whether g is increasing or decreasing in an interval around xo. g is decreasing in an interval around xo. g is zero in an interval around xo. O g is constant in an interval around xo. g is increasing in an interval around xo. (b) If f has a local maximum at x₁, what about g? g has a local maximum at x1. g has an inflection point at X₁. g has both a local minimum and a local maximum at x₁. We cannot tell whether g has a local minimum or a local maximum at x₁. Og has a local minimum at X₁. (c) If f is concave down at x2, what about g? O We cannot tell whether g is concave up or concave down at X2. Og is flat at X2. Og is concave up at X₂. O g is concave down at x₂. g is increasing at X2.
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