College Algebra (MindTap Course List)
12th Edition
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:R. David Gustafson, Jeff Hughes
Chapter3: Functions
Section3.3: More On Functions; Piecewise-defined Functions
Problem 99E: Determine if the statemment is true or false. If the statement is false, then correct it and make it...
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How do I do number 9
![2. Find the absolute extrema of f(x) = x + cot
(G)
on
3. If a and b are positive numbers, find the maximum value of f(x) = x°(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'(x) + 1 for all real
numbers x, then f has at most one fixed point.
6. Find a cubic function f(x) = ax³ + bx² + cx + d that has a local maximum value of 3 at x = -2 and
a local minimum value of 0 at x = 1.
7. Sketch the graph of a function ƒ that satisfies the following: f'(0) = f'(2) = f'(4) = 0, f'(x) > 0 if
x < 0 or 2 < < 4, f'(x) < 0 if 0 < x < 2 or x > 4, f"(x) > 0 if 1 < x < 3, and f"(x) < 0 if x < 1
or x > 3.
Evaluate the following limits:
8. lim (x
-
(4)
9. lim Tsin
r -o0
I +x +5
10. lim
3
+1
1](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F40a9514d-d7ca-4467-8320-3b6e9b54f257%2F50c95381-318f-4dd0-82fb-8909332f01ff%2F77cqshd_processed.png&w=3840&q=75)
Transcribed Image Text:2. Find the absolute extrema of f(x) = x + cot
(G)
on
3. If a and b are positive numbers, find the maximum value of f(x) = x°(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'(x) + 1 for all real
numbers x, then f has at most one fixed point.
6. Find a cubic function f(x) = ax³ + bx² + cx + d that has a local maximum value of 3 at x = -2 and
a local minimum value of 0 at x = 1.
7. Sketch the graph of a function ƒ that satisfies the following: f'(0) = f'(2) = f'(4) = 0, f'(x) > 0 if
x < 0 or 2 < < 4, f'(x) < 0 if 0 < x < 2 or x > 4, f"(x) > 0 if 1 < x < 3, and f"(x) < 0 if x < 1
or x > 3.
Evaluate the following limits:
8. lim (x
-
(4)
9. lim Tsin
r -o0
I +x +5
10. lim
3
+1
1
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