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(b) (2 points) use the Concavity Theorem to determine where f(x) is concave up and where it is concave down/Also find all inflection points. if f"x)>0 For all x in an open interval, then it is concave up on that interval. if fu(X)<0 For all x in an open interval, then it is concave down on thut in terval. f"(x) - 3x²-2x-6

(b) (2 points) use the Concavity Theorem to determine where f(x) is concave up and where it is concave down/Also find all inflection points. if f"x)>0 For all x in an open interval, then it is concave up on that interval. if fu(X)<0 For all x in an open interval, then it is concave down on thut in terval. f"(x) - 3x²-2x-6

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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Given the function f(x)= (x^4)/4-(x^3)/3-3x^2+10

use the Concavity Theorem to determine where f(x) is concave up and where it is concave down. Also find all inflection points. 

x+ 3. Given the function f(x) 4 - 3x² + 10 3 (a) (2 points) use the Monotonicity Theorem to find where f(x) is increasing and where it is decreasing. if f'x)>0for all x on the interval, then Fis increasing on that interval. if f'(x)<0 for all x on the interval, then is decreasing on that interval f'6x)= x'-x²- 6x » f(x) = x(x -3)(x+2) Critical pts: -2, 0, 3 3 + 이+ F(x) is increasing on (-2, 0) u (3, 0) Flx) is decreasing on (-00,-2) u(0, 3) (b) (2 points) use the Concavity Theorem to determine where f(x) is concave up and where it is concave down/Also find all inflection points. if f"x) >0 For all x in an open interval, then it is concave up on that interval. if f"CX)<O For all x in an open interval, then it is concave down on that interval. f"(x) = 3x²-2x-6
Transcribed Image Text:x+ 3. Given the function f(x) 4 - 3x² + 10 3 (a) (2 points) use the Monotonicity Theorem to find where f(x) is increasing and where it is decreasing. if f'x)>0for all x on the interval, then Fis increasing on that interval. if f'(x)<0 for all x on the interval, then is decreasing on that interval f'6x)= x'-x²- 6x » f(x) = x(x -3)(x+2) Critical pts: -2, 0, 3 3 + 이+ F(x) is increasing on (-2, 0) u (3, 0) Flx) is decreasing on (-00,-2) u(0, 3) (b) (2 points) use the Concavity Theorem to determine where f(x) is concave up and where it is concave down/Also find all inflection points. if f"x) >0 For all x in an open interval, then it is concave up on that interval. if f"CX)<O For all x in an open interval, then it is concave down on that interval. f"(x) = 3x²-2x-6
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