Question

A function is differentiable at \[x=c\] when which condition holds?

Options

• Only the left-hand derivative exists.

• Both one-sided derivatives exist, are finite, and are equal.

• The function is continuous only.

• Both one-sided derivatives are unequal.

Answer 1

Differentiability at a point requires both the left-hand derivative and right-hand derivative. They must exist, be finite, and have the same value.