1. Consider functions f, g: R → R that are continuous at every point in their domain. A. Sketch a graph of function f given that it has the following properties: f(0) = 1; - f(2)= -1; - ƒ' (0) = ƒ' (2) = 0; f is increasing on the intervals (-∞, 0] U [2, ∞); f is decreasing on the interval [0, 2]; f is concave down on the interval (-∞, 1]; f is concave up on the interval [1, ∞); f has an inflection point on the horizontal axis. - B. Sketch a graph of function g given that it has the following properties: g(-2) = 6; - g(1) = 2; - g(3) = 4; - g' (1) = g′ (3) = 0; For every a satisfying the inequality |¤ — 2| > 1, the value of g'(x) is negative; For every x satisfying the inequality |x − 2| < 1, the value of g'(x) is positive; - For every x satisfying either |x + 1| < 1 or x > 2, the value of g" (x) is negative; For every x satisfying either |x − 1| < 1 or x < −2, the value of g" (x) is positive.
1. Consider functions f, g: R → R that are continuous at every point in their domain. A. Sketch a graph of function f given that it has the following properties: f(0) = 1; - f(2)= -1; - ƒ' (0) = ƒ' (2) = 0; f is increasing on the intervals (-∞, 0] U [2, ∞); f is decreasing on the interval [0, 2]; f is concave down on the interval (-∞, 1]; f is concave up on the interval [1, ∞); f has an inflection point on the horizontal axis. - B. Sketch a graph of function g given that it has the following properties: g(-2) = 6; - g(1) = 2; - g(3) = 4; - g' (1) = g′ (3) = 0; For every a satisfying the inequality |¤ — 2| > 1, the value of g'(x) is negative; For every x satisfying the inequality |x − 2| < 1, the value of g'(x) is positive; - For every x satisfying either |x + 1| < 1 or x > 2, the value of g" (x) is negative; For every x satisfying either |x − 1| < 1 or x < −2, the value of g" (x) is positive.
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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![1. Consider functions f, g: R → R that are continuous at every point in their domain.
A. Sketch a graph of function
f given that it has the following properties:
- f(0) = 1;
- ƒ(2) = −1;
- ƒ' (0) = ƒ' (2) = 0;
-
f is increasing on the intervals (-∞, 0] U [2, ∞);
f is decreasing on the interval [0, 2];
f is concave down on the interval (-∞, 1];
- f is concave up on the interval [1, ∞);
- f has an inflection point on the horizontal axis.
B. Sketch a graph of function g given that it has the following properties:
- g(−2) = 6;
-
- g(1) = 2;
- g(3) = 4;
- g′ (1) = g′ (3) = 0;
For every x satisfying the inequality |x − 2| > 1, the value of g' (x) is negative;
For every x satisfying the inequality |x − 2| < 1, the value of g' (x) is positive;
For every
For every
satisfying either |x + 1| < 1 or ï > 2, the value of g" (x) is negative;
satisfying either |x − 1| < 1 or x < −2, the value of g" (x) is positive.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F0724d636-1660-41e9-be6d-29c03d60387f%2F0d51f588-cd09-4565-8a16-86e3b46f31a0%2Fkmzim9p_processed.png&w=3840&q=75)
Transcribed Image Text:1. Consider functions f, g: R → R that are continuous at every point in their domain.
A. Sketch a graph of function
f given that it has the following properties:
- f(0) = 1;
- ƒ(2) = −1;
- ƒ' (0) = ƒ' (2) = 0;
-
f is increasing on the intervals (-∞, 0] U [2, ∞);
f is decreasing on the interval [0, 2];
f is concave down on the interval (-∞, 1];
- f is concave up on the interval [1, ∞);
- f has an inflection point on the horizontal axis.
B. Sketch a graph of function g given that it has the following properties:
- g(−2) = 6;
-
- g(1) = 2;
- g(3) = 4;
- g′ (1) = g′ (3) = 0;
For every x satisfying the inequality |x − 2| > 1, the value of g' (x) is negative;
For every x satisfying the inequality |x − 2| < 1, the value of g' (x) is positive;
For every
For every
satisfying either |x + 1| < 1 or ï > 2, the value of g" (x) is negative;
satisfying either |x − 1| < 1 or x < −2, the value of g" (x) is positive.
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