JEE Math Practice Question

Let a function $$f: \mathbb{R} \rightarrow \mathbb{R}$$ be defined as : $$f(x)= \begin{cases}\int\limits_{0}^{x}(5-|t-3|) d t, & x>4 \\ x^{2}+b x & , x \leq 4\end{cases}$$ where $$\mathrm{b} \in \mathbb{R}$$. If $$f$$ is continuous at $$x=4$$, then which of the following statements is NOT true?

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