(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
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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Question
100%
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](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ffb25453d-2d1c-488c-803b-19812d304c79%2F8e0fdec8-a8eb-4b46-9bde-1009ba6e1e95%2Fjowhil_processed.jpeg&w=3840&q=75)
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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