A fixed point of a function f is a number in its domain such that f(c) =
Question:
(a) Sketch the graph of a continuous function with domain [0, 1] whose range also lies in [0, 1]. Locate a fixed point of f.
(b) Try to draw the graph of a continuous function with domain [0, 1] and range in [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 a subset of [0, 1] must have a fixed point.
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a Here are a few possibilities KA X y x Lonest b The obstacle is the line x y see di...View the full answer
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