Question

尼

81怎麼證明

f at (c, f(c)) is parallel to the tanger
81. Proof Prove that if f is differentiable on (-00,00) and
f'(x) < 1 for all real numbers
, then f has at most one fixed
point. [A fixed point of a function f is a real number c such
a
that f(c) = c.]
=
DA
TT
of Cvornica 81 to show that

Answer 1

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呵

因為 斜率恆小於1

所以 x的增加 不會造成 y急劇增加 以至於 兩次碰到x=y
x的減少同理

故 f has at most one fixed point