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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How do I do number 1
![Please show all of your work. As a reminder: you may feel free to work together on homework assignments,
but each student must turn in their own work.
1. Find the critical numbers of f(r) = 2 cos(x) + sin²(x)
(6) --
2. Find the absolute extrema of f(r) = x + cot
4 4
T 7元
on
3. If a and b are positive numbers, find the maximum value of f(x) = xª(1 - x°) on [0, 1].
4. Sam and Michael are running a race. They start at the same time, and the race between these
"high-caliber" athletes finishes in a tie. Show that at some point during the race, Sam and Michael
were running at the same speed.
5. A number a is called a fixed point of a function f if f(a) = a. Prove that if f'(r) # 1 for all real
numbers r, then f has at most one fixed point.
6. Find a cubic function f(r) = ar + bx? + cr+d that has a local maximum value of 3 at z -2 and
a local minimum value of 0 at z= 1.
7. Sketch the graph of a function f that satisfies the following: f'(0) = f'(2) = f'(4) = 0, f'(x) > 0 if
x < 0 or 2 < x < 4, f'(x) < 0 if 0 < x < 2 or a > 4, f"(x) > 0 if 1 < x < 3, and f"(r) < 0 if x < 1
or I > 3.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F40a9514d-d7ca-4467-8320-3b6e9b54f257%2F3453802a-7eb1-4a77-9b36-01af2e5026a8%2Fk85gqk_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Please show all of your work. As a reminder: you may feel free to work together on homework assignments,
but each student must turn in their own work.
1. Find the critical numbers of f(r) = 2 cos(x) + sin²(x)
(6) --
2. Find the absolute extrema of f(r) = x + cot
4 4
T 7元
on
3. If a and b are positive numbers, find the maximum value of f(x) = xª(1 - x°) on [0, 1].
4. Sam and Michael are running a race. They start at the same time, and the race between these
"high-caliber" athletes finishes in a tie. Show that at some point during the race, Sam and Michael
were running at the same speed.
5. A number a is called a fixed point of a function f if f(a) = a. Prove that if f'(r) # 1 for all real
numbers r, then f has at most one fixed point.
6. Find a cubic function f(r) = ar + bx? + cr+d that has a local maximum value of 3 at z -2 and
a local minimum value of 0 at z= 1.
7. Sketch the graph of a function f that satisfies the following: f'(0) = f'(2) = f'(4) = 0, f'(x) > 0 if
x < 0 or 2 < x < 4, f'(x) < 0 if 0 < x < 2 or a > 4, f"(x) > 0 if 1 < x < 3, and f"(r) < 0 if x < 1
or I > 3.
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