derivative and determine its range. in (a). Sketch the graph of the function using the first of is decreasing for x32 + (x) 36 (x+1)² prx<2. 0 »), 12 + (as its derivative and is a quacuatic parabole Range: (-00, 16] IC
derivative and determine its range. in (a). Sketch the graph of the function using the first of is decreasing for x32 + (x) 36 (x+1)² prx<2. 0 »), 12 + (as its derivative and is a quacuatic parabole Range: (-00, 16] IC
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
Only need question (c), and the answer is [15,16] but I don't know why
![3. Consider the function
f(x) =
az²+b, x<2
x ≥ 2
36
I+1¹
(a) Determine the numbers a and b so that y = f(x) is differentiable for all c.
Contatzi4a+b = 12
Diff. 4²1 4a = - 4
f(x) =
ť'
a=-1
{x)
=
f
I is decreasing
36
(x+1)²
2
x<2.
(b) Assume the values of a and b obtained in (a). Sketch the graph of the function f using the first
derivative and determine its range.
(as its derivative
x² +16
36
(x+1)
Las
b = 12-49 = 16
for x 22
<o)
range
12
x < 2
x>2
(c) Determine the range of the composite function y = f
arctanx has
(--플,풀.)
arctem x
range (-1, 1)
and is
arctan a
)
a
So
quacuatic pambule
Range: (-00, 16]
f(arctaux)
has range [15, 16]
10](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F02c99683-a01b-4e64-96f8-7137fedec6c4%2F12a2c965-15cb-4ac7-8adc-399fdfb835e4%2F830z3ft_processed.png&w=3840&q=75)
Transcribed Image Text:3. Consider the function
f(x) =
az²+b, x<2
x ≥ 2
36
I+1¹
(a) Determine the numbers a and b so that y = f(x) is differentiable for all c.
Contatzi4a+b = 12
Diff. 4²1 4a = - 4
f(x) =
ť'
a=-1
{x)
=
f
I is decreasing
36
(x+1)²
2
x<2.
(b) Assume the values of a and b obtained in (a). Sketch the graph of the function f using the first
derivative and determine its range.
(as its derivative
x² +16
36
(x+1)
Las
b = 12-49 = 16
for x 22
<o)
range
12
x < 2
x>2
(c) Determine the range of the composite function y = f
arctanx has
(--플,풀.)
arctem x
range (-1, 1)
and is
arctan a
)
a
So
quacuatic pambule
Range: (-00, 16]
f(arctaux)
has range [15, 16]
10
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