AP style question 6. Suppose f is a twice- differentiable function such that f(2) = 5 and f (5) = 2. Further suppose that g(x) = f(f(x)). a) Explain why there must be a value c for 2
AP style question 6. Suppose f is a twice- differentiable function such that f(2) = 5 and f (5) = 2. Further suppose that g(x) = f(f(x)). a) Explain why there must be a value c for 2
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:AP style question
6. Suppose f is a twice-
differentiable function
such that f(2) = 5 and
f (5) = 2. Further suppose
that g(x) = f(f(x)).
a) Explain why there
must be a value c for
2 <c < 5 such that
f'(c) = -1.
%3D
b) Find g'(x), g'(2), and
g'(5).
c) Using your results in
(b), explain why there
must be a value d for
2 < d < 5 such that
g"(5) = 0.
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