Question

Which of the following is a correct statement?

• A. Continuity at $x=a$ is sufficient for differentiability at $x=a$
• B. Differentiability at $x=a$ is sufficient for continuity at $x=a$
• C. Existence of limit at $x=a$ is sufficient for continuity at $x=a$
• D. Differentiability at $x=a$ is necessary for existence of tangent at $x=a$

Answer 1

Answer: (B)

If $f\left(x\right)$ is differentiable at $x=a$ , then $f\left(x\right)$ is also continuous at $x=a$
Hence, differentiability at $x=a$ is sufficient for continuity at $x=a$