7. \(\mathrm { f } ( x ) = x + \frac { \mathrm { e } ^ { x } } { 5 } , \quad x \in \mathbb { R }\).
- Find \(\mathrm { f } ^ { \prime } ( x )\).
The curve \(C\), with equation \(y = \mathrm { f } ( x )\), crosses the \(y\)-axis at the point \(A\).
- Find an equation for the tangent to \(C\) at \(A\).
- Complete the table, giving the values of \(\sqrt { \left( x + \frac { \mathrm { e } ^ { x } } { 5 } \right) }\) to 2 decimal places.
| \(x\) | 0 | 0.5 | 1 | 1.5 | 2 |
| \(\sqrt { \left( x + \frac { \mathrm { e } ^ { x } } { 5 } \right) }\) | 0.45 | 0.91 | | | |