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CalculusQ&A LibraryA fixed point of a function f is a number c in its domain such that f(c) = c. (a) Sketch the graph of a continuous function wih domain [0,1] whose range also lies in [0,1]. Locate a fixed point f . (b) Try to draw the graph of a continuous function with domain [0,1] and range [0,1] that does not have a fixed point. What is the obstacle? (c) Use the Intermediate Value Theorem to prove that any continuous function with domain [0,1] and range [0,1] must have a fixed point.Start your trial now! First week only $4.99!*arrow_forward*

Question

A fixed point of a function f is a number c in its domain such that f(c) = c.

(a) Sketch the graph of a continuous function wih domain [0,1] whose range also lies in

[0,1]. Locate a fixed point f .

(b) Try to draw the graph of a continuous function with domain [0,1] and range [0,1] that

does not have a fixed point. What is the obstacle?

(c) Use the Intermediate Value Theorem to prove that any continuous function with domain

[0,1] and range [0,1] must have a fixed point.

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Calculus

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