Let L(x) be the linearization of an arbitrary function f about c. Assume that f is concave down in an open interval I containing c. Which of the following statements is true? (1) f(x) > L(x) for all xe I (I1I) f(c) > L(c) (III) f(x) < L(x) for all xe I (IV) f(c) < L(c) (V) f(c) # L(c). only I OI and II I and V only II III and IV

Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter6: Vector Spaces
Section6.2: Linear Independence, Basis, And Dimension
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Let L(x) be the linearization of an arbitrary function f about c.
Assume that f is concave down in an open interval I containing c.
Which of the following statements is true?
(1) f(x) > L(x) for all xe I
(II) f(c) > L(c)
(III) f(x) < L(x) for all xe I
(IV) f(c) < L(c)
(V) f(c) # L(c).
O only I
OI and II
I and V
only III
IIlI and IV
Transcribed Image Text:Let L(x) be the linearization of an arbitrary function f about c. Assume that f is concave down in an open interval I containing c. Which of the following statements is true? (1) f(x) > L(x) for all xe I (II) f(c) > L(c) (III) f(x) < L(x) for all xe I (IV) f(c) < L(c) (V) f(c) # L(c). O only I OI and II I and V only III IIlI and IV
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