Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter4: Polynomial And Rational Functions
Section4.5: Rational Functions
Problem 54E
Related questions
Question
Determine whether Mean Value Theorem can be applied to f on the indicated interval. In each case, find all the the values of c in the interval (a, b) that satisfies the MVT. (Show work and step-by-step process in finding the correct answers.) #10 only!!
![8. S(2)=**:2|
9. f(x)= Vx-2; [2,6]
x+1
10. f(x) = sin x; [0, 7r ]
The table below gives selected values of x and f(x). The function f is a differentiable function.
Answer the questions below in complete sentences.
-3
-1
2
6.
-1
-4
-1
1
f(x) 3
11. Explain why there is a guaranteed value of c such that f'(c)=0 on the interval (-1, 2).
12. Is there a value of c in the interval (0, 5) where f'(c)=1? Justify your answer.
13. Is there a value of c in the interval (-1, 5) where f'(c)=3 ? Justify your answer.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F65ff4d60-b6ce-4f7b-89e6-d7df5a1ec7ee%2F08dad6cd-e3f5-4cf1-9e1e-0f114760f28f%2Fys5mejv_processed.jpeg&w=3840&q=75)
Transcribed Image Text:8. S(2)=**:2|
9. f(x)= Vx-2; [2,6]
x+1
10. f(x) = sin x; [0, 7r ]
The table below gives selected values of x and f(x). The function f is a differentiable function.
Answer the questions below in complete sentences.
-3
-1
2
6.
-1
-4
-1
1
f(x) 3
11. Explain why there is a guaranteed value of c such that f'(c)=0 on the interval (-1, 2).
12. Is there a value of c in the interval (0, 5) where f'(c)=1? Justify your answer.
13. Is there a value of c in the interval (-1, 5) where f'(c)=3 ? Justify your answer.
![Worksheet #4A: Rolle's and MVT
Name
Determine whether Rolle's Theorem can be applied to f on the indicated interval. If Rolle's Theorem can
be applied, find all the values of c in the interval that satisfies the Rolle's Theorem.
1. f(x)=x² -3x+2; [1,2]
2. f(x) =x-1; [-8,8]
3. f(x) =*-2-3,(-1,3]
4. f(x)=sin x; [0,27]
x+2
5. f(x) = sin 2.x;
Determine whether the Mean Value Theorem can be applied tof on the indicated interval. In each case,
find all values of c in the interval (a, b) that satisfies the MVT.
6. f(x) =x(x' -x-2):[(-1,1]
7. f(x) =x*; [0,1]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F65ff4d60-b6ce-4f7b-89e6-d7df5a1ec7ee%2F08dad6cd-e3f5-4cf1-9e1e-0f114760f28f%2F0xgkm5_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Worksheet #4A: Rolle's and MVT
Name
Determine whether Rolle's Theorem can be applied to f on the indicated interval. If Rolle's Theorem can
be applied, find all the values of c in the interval that satisfies the Rolle's Theorem.
1. f(x)=x² -3x+2; [1,2]
2. f(x) =x-1; [-8,8]
3. f(x) =*-2-3,(-1,3]
4. f(x)=sin x; [0,27]
x+2
5. f(x) = sin 2.x;
Determine whether the Mean Value Theorem can be applied tof on the indicated interval. In each case,
find all values of c in the interval (a, b) that satisfies the MVT.
6. f(x) =x(x' -x-2):[(-1,1]
7. f(x) =x*; [0,1]
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