Question

Which of the following is not true

• A. A polynomial function is always continuous
• B. A continuous function is always differentiable
• C. A differentiable function is always continuous
• D. $f(x) = \left\{ \begin{matrix} \left( x^{2} + e^{\frac{1}{2 - x}} \right)^{- 1} & , & x \neq 2 \\ k & , & x = 2 \end{matrix} \right.\$ is continuous for all x

Answer 1

Answer: (B)

A continuous function is always differentiable

Answer 2

A continuous function may or may not be differentiable. So (2) is not true.