Suppose that a function ƒ is continuous on the closed interval [0, 1] and that 0<=ƒ(x)<= 1 for every x in [0, 1] . Show that there must exist a number c in [0, 1] such that ƒ(c) = c (c is called a fixed point of ƒ).
Suppose that a function ƒ is continuous on the closed interval [0, 1] and that 0<=ƒ(x)<= 1 for every x in [0, 1] . Show that there must exist a number c in [0, 1] such that ƒ(c) = c (c is called a fixed point of ƒ).
Chapter3: Functions
Section3.3: Rates Of Change And Behavior Of Graphs
Problem 2SE: If a functionfis increasing on (a,b) and decreasing on (b,c) , then what can be said about the local...
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Suppose that a function ƒ is continuous on the closed interval [0, 1] and that 0<=ƒ(x)<= 1 for every x in [0, 1] .
Show that there must exist a number c in [0, 1] such that ƒ(c) = c (c is called a fixed point of ƒ).
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