ISI2015-MMA-69

Question

Consider the function $$f(x) = \begin{cases} \int_0^x \{5+ \mid 1-y \mid \} dy & \text{ if } x>2 \\ 5x+2 & \text{ if } x \leq 2 \end{cases}$$ Then

• A. $f$ is not continuous at $x=2$
• B. $f$ is continuous and differentiable everywhere
• C. $f$ is continuous everywhere but not differentiable at $x=1$
• D. $f$ is continuous everywhere but not differentiable at $x=2$