Chapter 1, Problem 25TFQ

Determine whether the statement is true or false. If it is true, explainwhy. If it is false, explain why or give an example that disproves thestatement.   All continuous functions have antiderivatives.

Determine whether the statement is true or false. If it is false, explain why or give an example that shows it is false. The Intermediate Value Theorem guarantees that f(a) and f(b) differ in sign when a continuous function f has at least one zero on [a, b].

Determine whether the statement is true or false. If it is false, explain why or give an example that shows it is false.                                                                If f(x) = g(x) for x ≠ c and f(c) ≠ g(c), then either f or g is not continuous at c.