w/ Given a function f: [a, b] → R. Suppose that f" (x) exists, and f(a) = f (a) = f (b) = 0. %3D Show that for any c E [a, b], there exists & E (a, b), such that: 1 f(c) = "(E)(c – a)²(c- b)
w/ Given a function f: [a, b] → R. Suppose that f" (x) exists, and f(a) = f (a) = f (b) = 0. %3D Show that for any c E [a, b], there exists & E (a, b), such that: 1 f(c) = "(E)(c – a)²(c- b)
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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![Given a function f : [a, b] → R. Suppose that f"(x) exists, and f(a) = f (a) = f(b) = 0.
Show that for any c e [a, b], there exists & E (a, b), such that:
f (c)
1
f"(E)(c – a)²(c – b)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fad7331c8-2785-479b-9131-addb1c160fd5%2Ff875ec59-55e6-4960-9629-0a4a3f5ab7c3%2Fu4a7zdd_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Given a function f : [a, b] → R. Suppose that f"(x) exists, and f(a) = f (a) = f(b) = 0.
Show that for any c e [a, b], there exists & E (a, b), such that:
f (c)
1
f"(E)(c – a)²(c – b)
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