7.
$$\mathrm { f } ( x ) = \frac { x ^ { 2 } + 3 } { 4 x + 1 } , \quad x \in \mathbb { R } , \quad x \neq - \frac { 1 } { 4 }$$
- Find and simplify an expression for \(\mathrm { f } ^ { \prime } ( x )\).
- Find the set of values of \(x\) for which \(\mathrm { f } ( x )\) is increasing.
- Use Simpson's rule with six strips to find an approximate value for
$$\int _ { 0 } ^ { 6 } f ( x ) d x$$