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4. Let f(x) = -2x³ + 5x² +4 a. Is f(x) increasing or decreasing at x = 2? Explain using f'(x) how you know. b. Is f(x) concave up or concave down at x = 3? Explain using f" (x) how you know. c. When does f(x) attain a relative max? a relative min? Explain using f'(x) how you know. d. When does f(x) attain a point of inflection? Explain using f"(x) how you know.

4. Let f(x) = -2x³ + 5x² +4 a. Is f(x) increasing or decreasing at x = 2? Explain using f'(x) how you know. b. Is f(x) concave up or concave down at x = 3? Explain using f" (x) how you know. c. When does f(x) attain a relative max? a relative min? Explain using f'(x) how you know. d. When does f(x) attain a point of inflection? Explain using f"(x) how you know.

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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Observations a. The point (3, 4) is on the graph of f'(x). Conclusions I. f(x) has a relative minimum point at x = 3. b. The point (3, 4) is on the graph of f (x). II. When x = 3, the graph of f(x) is concave up. c. The point (3, 4) is on the graph of f"(x). II. When x = 3, the tangent line to the graph of y = f(x) has slope 4. d. The point (3, 0) is on the graph of f"(x), and the point (3, 4) is on the graph of f"(x). IV. When x = 3, the value of f(x) is 4. e. The point (3, 0) is on the graph of f'" (x), and the point (3, -4) is on the graph of f"(x). V. f(x) has a relative maximum point at x = 3 4. Let f(x) = -2x³ + 5x² + 4 a. Is f(x) increasing or decreasing at x = 2? Explain using f'(x) how you know. b. Is f(x) concave up or concave down at x = 3? Explain using f" (x) how you know. c. When does f(x) attain a relative max? a relative min? Explain using f'(x) how you know. d. When does f(x) attain a point of inflection? Explain using f" (x) how you know.
Transcribed Image Text:Observations a. The point (3, 4) is on the graph of f'(x). Conclusions I. f(x) has a relative minimum point at x = 3. b. The point (3, 4) is on the graph of f (x). II. When x = 3, the graph of f(x) is concave up. c. The point (3, 4) is on the graph of f"(x). II. When x = 3, the tangent line to the graph of y = f(x) has slope 4. d. The point (3, 0) is on the graph of f"(x), and the point (3, 4) is on the graph of f"(x). IV. When x = 3, the value of f(x) is 4. e. The point (3, 0) is on the graph of f'" (x), and the point (3, -4) is on the graph of f"(x). V. f(x) has a relative maximum point at x = 3 4. Let f(x) = -2x³ + 5x² + 4 a. Is f(x) increasing or decreasing at x = 2? Explain using f'(x) how you know. b. Is f(x) concave up or concave down at x = 3? Explain using f" (x) how you know. c. When does f(x) attain a relative max? a relative min? Explain using f'(x) how you know. d. When does f(x) attain a point of inflection? Explain using f" (x) how you know.
Expert Solution
Step 1

(4) For any function f(x), if f'x<0 then the function is decreasing and for f'x>0 the function is increasing.

For any function f(x), if f''x<0 then the function is concave down and for f''x>0 the function is concave up.

If at the critical points the value for f''x<0 then, the critical point x is the point of relative minimum. For f''x>0 the critical point x is the point of relative maximum.

The point of inflection is calculated by solving the equation f''x=0 for the value for x.

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