3. Suppose f(x) = x ^ 4 - 4x ^ 2 + 6, and g(x) = 3x ^ 3 - 8x. Prove, via the %3D %3D Intermediate Value Theorem, that the functions intersect at least twice between x = -2 and x = 4.
3. Suppose f(x) = x ^ 4 - 4x ^ 2 + 6, and g(x) = 3x ^ 3 - 8x. Prove, via the %3D %3D Intermediate Value Theorem, that the functions intersect at least twice between x = -2 and x = 4.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![3. Suppose f(x) = x ^ 4 - 4x ^ 2 + 6, and g(x) = 3x ^ 3 - 8x. Prove, via the
Intermediate Value Theorem, that the functions intersect at least twice between x
-2 and x =
%3D
4. Suppose f(x) is continuous on the interval [0,1] with 0< = f(x)< = 1 for all x.
Prove that f has a fixed point; that is, there exists a c in the interval [0,1] such that
f(c) = c. (Hint: You need to use the Intermediate Value Theorem on the function
h(x) = f(x) – x.)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa2e50573-b000-490e-892a-bd3af2ad7850%2F61da17dc-d2e7-4cd0-b4a9-fb813f2ceb25%2Fsrdmxl8_processed.jpeg&w=3840&q=75)
Transcribed Image Text:3. Suppose f(x) = x ^ 4 - 4x ^ 2 + 6, and g(x) = 3x ^ 3 - 8x. Prove, via the
Intermediate Value Theorem, that the functions intersect at least twice between x
-2 and x =
%3D
4. Suppose f(x) is continuous on the interval [0,1] with 0< = f(x)< = 1 for all x.
Prove that f has a fixed point; that is, there exists a c in the interval [0,1] such that
f(c) = c. (Hint: You need to use the Intermediate Value Theorem on the function
h(x) = f(x) – x.)
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