Suppose f: R → R is continuously differentiable. Show that if f'(x) > 0 for xo R, then there exists some interval I = (xo - 8, xo + 6) such that f|, : I → j bijective.

Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
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Chapter6: Vector Spaces
Section6.5: The Kernel And Range Of A Linear Transformation
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This problem introduces a very reduced version of the inverse function theorem.

Suppose f R → R is continuously differentiable. Show that if f'(x) > 0 for some
xo R, then there exists some interval I = (xo − 6, xo + 6) such that ƒ|, : I → ƒ(I) is
bijective.
Transcribed Image Text:Suppose f R → R is continuously differentiable. Show that if f'(x) > 0 for some xo R, then there exists some interval I = (xo − 6, xo + 6) such that ƒ|, : I → ƒ(I) is bijective.
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