Piecewise function with an integral piece: continuity and differentiability

1. A.
   $f(x)$ is differentiable $\forall x \in R$
2. B.
   $f(x)$ is continuous at $x = 2$ but not differentiable at $x = 2$
3. C.
   $f(x)$ is continuous at $x = 2$ but not differentiable at $x = 1$
4. D.
   none of these

Tap an option to check your answer.

1. A.
   $f$ is not differentiable at $x = 4$
2. B.
   $f'(3) + f'(5) = \frac{35}{4}$
3. C.
   $f$ is increasing in $\left( - \infty,\frac{1}{8} \right) \cup (8,\infty)$
4. D.
   $f$ has a local minima at $x = \frac{1}{8}$

Tap an option to check your answer.