1. The problem asks to determine the truth value of the statement: "If $f$ is differentiable on $[-1,1]$ then $f$ is continuous at $x=0$." 2. Recall the important rule: Differentiability at a point implies continuity at that point. 3. Since $f$ is differentiable on the entire interval $[-1,1]$, it is differentiable at $x=0$. 4. Therefore, $f$ must be continuous at $x=0$. 5. Hence, the statement is True. Final answer: True