Question

All continuous functions have antiderivatives.

Short answer

The answer is TRUE.

Step-by-step solution

Step 1: The Fundamental Theorem of Calculus.

From the Fundamental Theorem, Part 1, if f is continuous on an interval (a,b), then the function g is defined by:

Part 1: \(If\;g(x) = \int\limits_a^x {f\left( t \right)dt,\;then\;g'(x) = f(x)} \)

Step 2: Explanation

As we can see \(g(x) = \int\limits_a^x {f\left( t \right)dt} \) (a,b) is an antiderivative of f or \(g'(x) = f(x)\) for a<x<b of(a,b).

Looking at the question, the statement of the question is already implied by the Fundamental Theorem of Calculus which guarantees the existence of an antiderivative for a function f that is continuous on the interval (a,b). Hence, the statement is TRUE.