6:13 Back HW 9 - written component 3 of 3 Question 1 Determine whether Rolle's Theorem applies to the following functions on the given interval. If so, find the point(s) guaranteed to exist by Rolle's Theorem. If the theorem does not apply, clearly explain why. (a) f(x)=x³-x²-5x-3, on [-1,3] (b) f(x)=x+(1-x)2/3, on (-1,3] (c) f(x) = 1 − |x|, on [−1, 1] Question 2 Let f(x)=3x+cosx-sin. Show that f(x) has an unique root. Question 3 Assume f is a differentiable function on [1, 5]. Assume that f(1) = -2 and that f'(x) ≥ 12 for all r = [1,5]. What is the smallest f(5) can be? Question 4 Determine whether M.V.T. applies to the following functions on the given interval. If so, find the point(s) guaranteed to exist by M.V.T.. If the theorem does not apply, clearly explain why. (a) f(x)=2x+√x-1, on [1,5] 2-3 (b) f(x) = on [0,4] 1- (c) f(x)=√3x+2cos z, on [0,2] (d) f(x) = x²-³, on [−1,1] 20
6:13 Back HW 9 - written component 3 of 3 Question 1 Determine whether Rolle's Theorem applies to the following functions on the given interval. If so, find the point(s) guaranteed to exist by Rolle's Theorem. If the theorem does not apply, clearly explain why. (a) f(x)=x³-x²-5x-3, on [-1,3] (b) f(x)=x+(1-x)2/3, on (-1,3] (c) f(x) = 1 − |x|, on [−1, 1] Question 2 Let f(x)=3x+cosx-sin. Show that f(x) has an unique root. Question 3 Assume f is a differentiable function on [1, 5]. Assume that f(1) = -2 and that f'(x) ≥ 12 for all r = [1,5]. What is the smallest f(5) can be? Question 4 Determine whether M.V.T. applies to the following functions on the given interval. If so, find the point(s) guaranteed to exist by M.V.T.. If the theorem does not apply, clearly explain why. (a) f(x)=2x+√x-1, on [1,5] 2-3 (b) f(x) = on [0,4] 1- (c) f(x)=√3x+2cos z, on [0,2] (d) f(x) = x²-³, on [−1,1] 20
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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Solutions to question 1 please
![6:13
Back HW 9 - written component
3 of 3
Question 1
Determine whether Rolle's Theorem applies to the following functions on the given interval.
If so, find the point(s) guaranteed to exist by Rolle's Theorem. If the theorem does not apply,
clearly explain why.
(a) f(x)=x³-x²-5x-3, on [-1,3]
(b) f(x)=x+(1-x)2/3, on (-1,3]
(c) f(x) = 1 − |x|, on [−1, 1]
Question 2
Let f(x)=3x+cosx-sin. Show that f(x) has an unique root.
Question 3
Assume f is a differentiable function on [1, 5]. Assume that f(1) = -2 and that f'(x) ≥ 12 for
all r = [1,5]. What is the smallest f(5) can be?
Question 4
Determine whether M.V.T. applies to the following functions on the given interval. If so, find
the point(s) guaranteed to exist by M.V.T.. If the theorem does not apply, clearly explain why.
(a) f(x)=2x+√x-1, on [1,5]
2-3
(b) f(x) =
on [0,4]
1-
(c) f(x)=√3x+2cos z, on [0,2]
(d) f(x) = x²-³, on [−1,1]
20](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa7634a6a-5ecc-40e2-9892-46ba7a4cefd4%2Fff130222-ffcc-45c4-8de7-99c06e2179b8%2Fluler15_processed.jpeg&w=3840&q=75)
Transcribed Image Text:6:13
Back HW 9 - written component
3 of 3
Question 1
Determine whether Rolle's Theorem applies to the following functions on the given interval.
If so, find the point(s) guaranteed to exist by Rolle's Theorem. If the theorem does not apply,
clearly explain why.
(a) f(x)=x³-x²-5x-3, on [-1,3]
(b) f(x)=x+(1-x)2/3, on (-1,3]
(c) f(x) = 1 − |x|, on [−1, 1]
Question 2
Let f(x)=3x+cosx-sin. Show that f(x) has an unique root.
Question 3
Assume f is a differentiable function on [1, 5]. Assume that f(1) = -2 and that f'(x) ≥ 12 for
all r = [1,5]. What is the smallest f(5) can be?
Question 4
Determine whether M.V.T. applies to the following functions on the given interval. If so, find
the point(s) guaranteed to exist by M.V.T.. If the theorem does not apply, clearly explain why.
(a) f(x)=2x+√x-1, on [1,5]
2-3
(b) f(x) =
on [0,4]
1-
(c) f(x)=√3x+2cos z, on [0,2]
(d) f(x) = x²-³, on [−1,1]
20
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