(3) Consider f(x) = 2x³ + x² - 4x + 1 (a) Find decreasing and increasing intervals of f(x) f'(x) = 6x² + 5x -4 Need critical points ? f'w=0 6x² +5x-4-0 (factor expression) (3x²+ 2x+x-2)=0 <(+2)(-+)² No + correct 3042:0 3x =-2 12x 75 = 0 x=1 K (b) Find concave up and concave down intervals of f(x) Concavily you use the seconde derivative f"(x) = 6x² + 5x-4 = 12x +5 12x=-5 x = -5 Increasing: (-0, $) U (1,00) factoring (Decreasing: (1,5) ,5) Concave up when F) 200 Concave down when FW 20 € (0,0) (c) Find the x-coordinate of any inflection points. snflection rainko one az ? fex) | points (+) (+) ه عله بر 5/8 2 % come from 2nd derivative %2
(3) Consider f(x) = 2x³ + x² - 4x + 1 (a) Find decreasing and increasing intervals of f(x) f'(x) = 6x² + 5x -4 Need critical points ? f'w=0 6x² +5x-4-0 (factor expression) (3x²+ 2x+x-2)=0 <(+2)(-+)² No + correct 3042:0 3x =-2 12x 75 = 0 x=1 K (b) Find concave up and concave down intervals of f(x) Concavily you use the seconde derivative f"(x) = 6x² + 5x-4 = 12x +5 12x=-5 x = -5 Increasing: (-0, $) U (1,00) factoring (Decreasing: (1,5) ,5) Concave up when F) 200 Concave down when FW 20 € (0,0) (c) Find the x-coordinate of any inflection points. snflection rainko one az ? fex) | points (+) (+) ه عله بر 5/8 2 % come from 2nd derivative %2
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...
Related questions
Question
can i have help with these questions please
![6
(d) Find any relative maxima and minima using the first derivative test. (Justify your answer)
ficx) 6x² +5x-4
6x² +5x -4 = 0
2 (3x² - 2x-xx-2)=0
<^^x)=0) ?
2
(3x+2) =0
Relative max
0 112
value of 30
x=2
-> How?
zero ?
No relative value since everything is.
f"(x) = 12x + 5
12x +5=0
12x = -5
(e) Find any relative maxima and minima using the second derivative test. (Justify your answer)
A
aweb wwabnos bas qurosond
x = = 15/2
12 (1)+5=1
No relative
it equals to zove
тах со
Relative min value of o @ x =
15/2
ਕਰਦੇ
1/6
How 7
DAW7
1½
2/12](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F2b0c6e1e-4199-4748-a3ac-b4011616d8c3%2F1b79b943-2d79-4352-9ab5-a72ca51c7dc7%2Ftn5unon_processed.jpeg&w=3840&q=75)
Transcribed Image Text:6
(d) Find any relative maxima and minima using the first derivative test. (Justify your answer)
ficx) 6x² +5x-4
6x² +5x -4 = 0
2 (3x² - 2x-xx-2)=0
<^^x)=0) ?
2
(3x+2) =0
Relative max
0 112
value of 30
x=2
-> How?
zero ?
No relative value since everything is.
f"(x) = 12x + 5
12x +5=0
12x = -5
(e) Find any relative maxima and minima using the second derivative test. (Justify your answer)
A
aweb wwabnos bas qurosond
x = = 15/2
12 (1)+5=1
No relative
it equals to zove
тах со
Relative min value of o @ x =
15/2
ਕਰਦੇ
1/6
How 7
DAW7
1½
2/12
![(3) Consider f(x) = 2x³ + x² - 4x + 1
(a) Find decreasing and increasing intervals of f(x)
f'(x) =
Need critical points
f'(x=0
6x²+5x-4 = 0 (factor expression)
Not
(3 (³x² + 2x + x - 2) = 0
< (23)+2) (x - 1)2 Not corred
correct
factoring
3xx72=0
X=1
?
کے دو
= 6x² + 5x - 4
3x =-2
=
a/n
f"(x) = 6x² + 5x-4
= 12x +5
12x +5 = 0
дл
(b) Find concave up and concave down intervals of f(x)
Concavily you use the second derivative
12x=05
12
x = 3/2
Increasing: (-00, $) U (1,0)
Decreasing:
دنا
Concave
up
Concave down when FW 20
$1
when FW) 20 (-∞, 32)
F(x)
too,
9)
IS
(c) Find the x-coordinate of any inflection points,
Inflection points are
وال
Als be
sale of
5/8
als
"C
points
(+)
(0%
2
=
come from 2nd derivative
6/
9/2](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F2b0c6e1e-4199-4748-a3ac-b4011616d8c3%2F1b79b943-2d79-4352-9ab5-a72ca51c7dc7%2Fap3lwx9_processed.jpeg&w=3840&q=75)
Transcribed Image Text:(3) Consider f(x) = 2x³ + x² - 4x + 1
(a) Find decreasing and increasing intervals of f(x)
f'(x) =
Need critical points
f'(x=0
6x²+5x-4 = 0 (factor expression)
Not
(3 (³x² + 2x + x - 2) = 0
< (23)+2) (x - 1)2 Not corred
correct
factoring
3xx72=0
X=1
?
کے دو
= 6x² + 5x - 4
3x =-2
=
a/n
f"(x) = 6x² + 5x-4
= 12x +5
12x +5 = 0
дл
(b) Find concave up and concave down intervals of f(x)
Concavily you use the second derivative
12x=05
12
x = 3/2
Increasing: (-00, $) U (1,0)
Decreasing:
دنا
Concave
up
Concave down when FW 20
$1
when FW) 20 (-∞, 32)
F(x)
too,
9)
IS
(c) Find the x-coordinate of any inflection points,
Inflection points are
وال
Als be
sale of
5/8
als
"C
points
(+)
(0%
2
=
come from 2nd derivative
6/
9/2
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