(a) (b) Suppose f() is convex on the interval [a,y] CR, and there's a point 3 such that a
(a) (b) Suppose f() is convex on the interval [a,y] CR, and there's a point 3 such that a
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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![Problem 2.
(a)
Suppose f() is convex on the interval [a, y] CR, and there's a point 3 such that
a <B<y. Show that
(b)
f(B) - f(a)
B - a
ƒ(y) — f(a)
7-α
<
f(y)-f(³)
7-B
(1)
If f() is smooth and convex on the interval [a, y] CR. Show that f() is Lipschitz
continious on (a, y) for some positive constant L, i.e.,
|f(x) = f(y)| ≤ Lx - y, Vx, y = (a, y).
-](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F747ab200-c676-4ed9-b814-dae7641fcf0c%2F873f68aa-670c-4b2a-9acc-9658cc0d578b%2Fnrcedgg_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Problem 2.
(a)
Suppose f() is convex on the interval [a, y] CR, and there's a point 3 such that
a <B<y. Show that
(b)
f(B) - f(a)
B - a
ƒ(y) — f(a)
7-α
<
f(y)-f(³)
7-B
(1)
If f() is smooth and convex on the interval [a, y] CR. Show that f() is Lipschitz
continious on (a, y) for some positive constant L, i.e.,
|f(x) = f(y)| ≤ Lx - y, Vx, y = (a, y).
-
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