Suppose f'(z) is continuous over an interval 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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Transcribed Image Text:Suppose f'(z) is continuous over an interval a <I< b, and a <c<d<b.
If f'(c) 5, then (check all that apply)
O f(c) = 5
Of(c) exists
Of(r) is increasing through z c
Of(z) is decreasing through z =c
Of does not have a minimum at z =c
Of does not have a maximum at zr =c
If f'(d) =
3, then (check all that apply)
Of(x) is decreasing through zr =d
Of(d)
-3
O f(r) is increasing throughr
O f does not have a minimum atI=d
Of(d) exists
Of does not have a maximum at I=d
Based on this, we know that for some z between I = c and r = d:
Of has a minimum
Of(x)- 0
Of does not exist
Of has a maximum
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