Question

If \( f(x) \) is a differentiable function in \( x \), then it is _____ .

• A. Unbounded
• B. Bounded
• C. Single Valued
• D. Continuous

Hint:

In calculus, remember that differentiability implies continuity, but continuity does not imply differentiability.

Answer 1

The Correct Option is D

If \( f(x) \) is a differentiable function in \( x \), then it is **continuous**. This is a fundamental result from calculus, as differentiability implies continuity. More specifically, for a function to be differentiable at a point, it must also be continuous at that point. However, the converse is not true: a continuous function need not be differentiable. In this case, we can conclude that since \( f(x) \) is differentiable, it must also be continuous at every point where it is defined.