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.
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.
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 4
![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(r) + sin2(x)
() -- :
T 77
4 4
2. Find the absolute extrema of f(x) x+ cot
3. If a and b are positive numbers, find the maximum value of f(r) = x"(1 – r°) 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'(a) +1 for all real
numbers r, then f has at most one fixed point.
6. Find a cubic function f(r) = ar' +br + cr+d that has a local maximum value of 3 at r -2 and
a local minimum value of 0 at r = 1.
7. Sketch the graph of a function f that satisfies the following: f'(0) = f'(2) = f'(4) = 0, f'(x) > 0 if
I < 0 or 2 < r < 4, f'(x) < 0 if 0 < z < 2 or x > 4, f"(x) > 0 if 1<x< 3, and f"(x) < 0 if z < 1
or z > 3.
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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(r) + sin2(x)
() -- :
T 77
4 4
2. Find the absolute extrema of f(x) x+ cot
3. If a and b are positive numbers, find the maximum value of f(r) = x"(1 – r°) 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'(a) +1 for all real
numbers r, then f has at most one fixed point.
6. Find a cubic function f(r) = ar' +br + cr+d that has a local maximum value of 3 at r -2 and
a local minimum value of 0 at r = 1.
7. Sketch the graph of a function f that satisfies the following: f'(0) = f'(2) = f'(4) = 0, f'(x) > 0 if
I < 0 or 2 < r < 4, f'(x) < 0 if 0 < z < 2 or x > 4, f"(x) > 0 if 1<x< 3, and f"(x) < 0 if z < 1
or z > 3.
A Download
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