Suppose a certain real-valued function f is continuous on the interval [33, 50] and differentiable on (33,50). Moreover, suppose we also know f'(x) ≤ 96, for all x € (33,50), and f(47) = 14. (a) We wish to find an explicit upper bound for f(50). Complete the following proof: Proof. First, since f is continuous on the interval Click for List and differentiable on Click for List then, by Click for List Click for List f(50)-f(47) = f'(c). = 50-47 Rearranging this and applying our assumptions on f, we conclude that f(50) = f(47) +3f' (c) ≤ 14+3 × 96 = 302. This completes the proof. (b) Using a similar argument, prove that f(33) > -1330 in the essay box below.
Suppose a certain real-valued function f is continuous on the interval [33, 50] and differentiable on (33,50). Moreover, suppose we also know f'(x) ≤ 96, for all x € (33,50), and f(47) = 14. (a) We wish to find an explicit upper bound for f(50). Complete the following proof: Proof. First, since f is continuous on the interval Click for List and differentiable on Click for List then, by Click for List Click for List f(50)-f(47) = f'(c). = 50-47 Rearranging this and applying our assumptions on f, we conclude that f(50) = f(47) +3f' (c) ≤ 14+3 × 96 = 302. This completes the proof. (b) Using a similar argument, prove that f(33) > -1330 in the essay box below.
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
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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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![(b) Using a similar argument, prove that f(33) > -1330 in the essay box below.
Essay box advice: There is no need to use correct Maple syntax or use the equation editor in the essay box
below, as long as your response is clear enough for a reader.
For example,
●
f(x) may be written as 'f(x)',
●
f'(c) may be written as 'f'(c)',
●
and may be written as '<=' and '>=', respectively,
a+b
●
may be written as '(a+b)/(c+d)',
c+d
• The intervals [0, 1] and (2, 3) may be written as '[0,1]' and '(2,3)', respectively.
Ga
三 = =
Equation
ΩΣ Editor
A-A-T
BIUS X₂ X²
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Styles](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F711d5420-a7c2-4b25-ac6b-803040d3da87%2F4eeff0f1-5856-41d1-a9a4-d2ad25228463%2Ffjqpee_processed.jpeg&w=3840&q=75)
Transcribed Image Text:(b) Using a similar argument, prove that f(33) > -1330 in the essay box below.
Essay box advice: There is no need to use correct Maple syntax or use the equation editor in the essay box
below, as long as your response is clear enough for a reader.
For example,
●
f(x) may be written as 'f(x)',
●
f'(c) may be written as 'f'(c)',
●
and may be written as '<=' and '>=', respectively,
a+b
●
may be written as '(a+b)/(c+d)',
c+d
• The intervals [0, 1] and (2, 3) may be written as '[0,1]' and '(2,3)', respectively.
Ga
三 = =
Equation
ΩΣ Editor
A-A-T
BIUS X₂ X²
Font
Size
Styles
![Suppose a certain real-valued function f is continuous on the interval [33, 50] and differentiable on (33,50).
Moreover, suppose we also know
f'(x) ≤ 96, for all x € (33,50), and f(47) = 14.
(a) We wish to find an explicit upper bound for f(50). Complete the following proof:
Proof. First, since f is continuous on the interval Click for List
and differentiable on Click for List
then, by Click for List
Click for List
f(50)-f(47) = f'(c).
50-47
Rearranging this and applying our assumptions on f, we conclude that
f(50) = f(47) +3f' (c) ≤ 14+3 × 96 = 302.
This completes the proof.
(b) Using a similar argument, prove that f(33) ≥-1330 in the essay box below.
Essay box advice: There is no need to use correct Maple syntax or use the equation editor in the essay box
below, as long as your response is clear enough for a reader.
For example,
• f(x) may be written as 'f(x)',
●
f'(c) may be written as 'f'(c)',
●
and may be written as '<=' and '>=', respectively,
a+b
may be written as '(a+b)/(c+d)',
c+d
10 11 ond ? 3) respectively.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F711d5420-a7c2-4b25-ac6b-803040d3da87%2F4eeff0f1-5856-41d1-a9a4-d2ad25228463%2Fbgr1g6_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Suppose a certain real-valued function f is continuous on the interval [33, 50] and differentiable on (33,50).
Moreover, suppose we also know
f'(x) ≤ 96, for all x € (33,50), and f(47) = 14.
(a) We wish to find an explicit upper bound for f(50). Complete the following proof:
Proof. First, since f is continuous on the interval Click for List
and differentiable on Click for List
then, by Click for List
Click for List
f(50)-f(47) = f'(c).
50-47
Rearranging this and applying our assumptions on f, we conclude that
f(50) = f(47) +3f' (c) ≤ 14+3 × 96 = 302.
This completes the proof.
(b) Using a similar argument, prove that f(33) ≥-1330 in the essay box below.
Essay box advice: There is no need to use correct Maple syntax or use the equation editor in the essay box
below, as long as your response is clear enough for a reader.
For example,
• f(x) may be written as 'f(x)',
●
f'(c) may be written as 'f'(c)',
●
and may be written as '<=' and '>=', respectively,
a+b
may be written as '(a+b)/(c+d)',
c+d
10 11 ond ? 3) respectively.
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