Question

answer the following true or false: if f(x) is a differentiable function at x = -6, then lim_{x→ - 6} f(x) exists. true false question help: message instructor

Explanation:

Step1: Recall differentiability - continuity relationship

If a function $f(x)$ is differentiable at a point $x = a$, then it is continuous at that point. The definition of continuity at $x=a$ is $\lim_{x
ightarrow a}f(x)=f(a)$. So if $f(x)$ is differentiable at $x=- 6$, it is continuous at $x = - 6$. And if a function is continuous at a point, the limit as $x$ approaches that point exists.

Answer:

True