Let f be continuous on an interval [a, b] and differentiable on the open interval (a, b). If f'(x) > 0 for every x € (a, b), then we can conclude that (select all that apply): f is strictly decreasing on [a, b]. For every 1,02 € (a, b) f(x₂) - f(x1) f'(x) = X2 X1 - with x₁ < 2, there is an x = (₁, 2) at which f is strictly increasing on (a, b). Of is decreasing on [a, b]. f is a constant function on [a, b]. Of is increasing on (a, b).
Let f be continuous on an interval [a, b] and differentiable on the open interval (a, b). If f'(x) > 0 for every x € (a, b), then we can conclude that (select all that apply): f is strictly decreasing on [a, b]. For every 1,02 € (a, b) f(x₂) - f(x1) f'(x) = X2 X1 - with x₁ < 2, there is an x = (₁, 2) at which f is strictly increasing on (a, b). Of is decreasing on [a, b]. f is a constant function on [a, b]. Of is increasing on (a, 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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![Let f be continuous on an interval [a, b] and differentiable on the open
interval (a, b). If f'(x) > 0 for every x € (a, b), then we can conclude
that (select all that apply):
f is strictly decreasing on [a, b].
For every 1,02 € (a, b) with ₁ < x2, there is an x = (₁, 2) at which
f(x₂)-f(x₁)
ƒ'(x)
X2 - X1
=
f is strictly increasing on (a, b).
Of is decreasing on [a, b].
Of is a constant function on [a, b].
Of is increasing on (a, b).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F44f6e5f3-0688-4380-ac70-a4dd557ffbc7%2F4b1e4ade-638d-4139-8531-69b2204817a4%2Fhgaeu0t_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Let f be continuous on an interval [a, b] and differentiable on the open
interval (a, b). If f'(x) > 0 for every x € (a, b), then we can conclude
that (select all that apply):
f is strictly decreasing on [a, b].
For every 1,02 € (a, b) with ₁ < x2, there is an x = (₁, 2) at which
f(x₂)-f(x₁)
ƒ'(x)
X2 - X1
=
f is strictly increasing on (a, b).
Of is decreasing on [a, b].
Of is a constant function on [a, b].
Of is increasing on (a, b).
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