( optional). Let f be continuous on [a, b] and differentiable in (a, 6). Show that if lim f'6) = A, then f'la) exists and equals A. Hint: Use the definition of f'la) and the mean value Theorem. )
( optional). Let f be continuous on [a, b] and differentiable in (a, 6). Show that if lim f'6) = A, then f'la) exists and equals A. Hint: Use the definition of f'la) and the mean value Theorem. )
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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![prove
10. (optional) Let f be coutianous on La, b]
and differentiable in (a, b).
if lim f'6) = A, then
Show that
f'la) exists
and equals A.
(Hìnt: Use the definition of f'la) and the
mean value Theorem. )](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb2b71fb6-0c5b-4ee8-9b09-d28169e9d364%2Ffd3b8414-62d2-4674-aa19-4cfca5d270e2%2F3anb6s8_processed.jpeg&w=3840&q=75)
Transcribed Image Text:prove
10. (optional) Let f be coutianous on La, b]
and differentiable in (a, b).
if lim f'6) = A, then
Show that
f'la) exists
and equals A.
(Hìnt: Use the definition of f'la) and the
mean value Theorem. )
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