textbook-theory · English
Some Consequences Of Continuity
Section 2.5 of the open textbook 'Difference Equations to Differential Equations' by Dan Sloughter, covering two fundamental consequences of continuity: the Intermediate Value Theorem and the Extreme Value Theorem. The section presents the bisection algorithm as a practical method for approximating roots of continuous functions on closed intervals, with worked numerical examples including root-finding for x^5 + x = 1 and optimization of a rectangular fencing problem. Practice problems reinforce both theorems and their computational applications.
Intermediate Value TheoremExtreme Value Theorembisection algorithmoptimization