MathematicsMedium210×since 2002Q3441Let a function f:R→Rf: \mathbb{R} \rightarrow \mathbb{R}f:R→R be defined as : f(x)={∫0x(5−∣t−3∣)dt,x>4x2+bx,x≤4f(x)= \begin{cases}\int\limits_{0}^{x}(5-|t-3|) d t, & x>4 \\ x^{2}+b x & , x \leq 4\end{cases}f(x)=⎩⎨⎧0∫x(5−∣t−3∣)dt,x2+bxx>4,x≤4 where b∈R\mathrm{b} \in \mathbb{R}b∈R. If fff is continuous at x=4x=4x=4, then which of the following statements is NOT true?Afff is not differentiable at x=4x=4x=4Bf′(3)+f′(5)=354f^{\prime}(3)+f^{\prime}(5)=\frac{35}{4}f′(3)+f′(5)=435Cfff is increasing in (−∞,18)∪(8,∞)\left(-\infty, \frac{1}{8}\right) \cup(8, \infty)(−∞,81)∪(8,∞)Dfff has a local minima at x=18x=\frac{1}{8}x=81Check answerSkip