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Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) §2.7 Continuous Functions, #43 · Calculus · Continuity

If … is continuous and … for all …, then there is…

If $f (x)$ is continuous and $0 \leq f (x) \leq 1$ for all $x$ , then there is a point where $f (x^{*}) = x^{*}$ . Explain with a graph and prove with the intermediate value theorem.

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Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) · §2.7 Continuous Functions, #43

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