1. **Problem:** Determine if the statement "If f is differentiable on [-1,1] then f is continuous at x = 0" is true. 2. **Recall the theorem:** Differentiability implies continuity. If a function $f$ is differentiable at a point $x = c$, then $f$ is continuous at $x = c$. 3. **Explanation:** Differentiability means the derivative $f'(c)$ exists, which requires the limit $$\lim_{h \to 0} \frac{f(c+h) - f(c)}{h}$$ to exist. 4. For this limit to exist, the function values $f(c+h)$ must approach $f(c)$ as $h \to 0$, which is the definition of continuity at $c$. 5. Since $f$ is differentiable on the interval $[-1,1]$, it is differentiable at every point in that interval, including $x=0$. 6. Therefore, $f$ must be continuous at $x=0$. **Final answer:** The statement is true.