Let a function f:ℝ→ℝ be defined as: fx=∫0x5-t-3dt,x>4x2+bx,x≤4 where b∈ℝ. If f is continuous at x=4, then which of the following statements is NOT true?

Question

Let a function $f : ℝ \to ℝ$ be defined as:

$f (x) = \{\begin{cases} \int_{0}^{x} (5 - |t - 3|) d t, & x > 4 \\ x^{2} + b x, & x \leq 4 \end{cases}$

where $b \in ℝ$ . If $f$ is continuous at $x = 4$ , then which of the following statements is NOT true?

f

is not differentiable at

x = 4

f^{'} (3) + f^{'} (5) = \frac{35}{4}

f

is increasing in

(- \infty, \frac{1}{8}) \cup (8, \infty)

f

has a local minima at

x = \frac{1}{8}

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