6 In this question you must show detailed reasoning.
- Given that \(y = \mathrm { e } ^ { 2 x } - 8 \mathrm { e } ^ { x } - 16 x ^ { 2 } + 7 x - 3\), determine the range of values of \(x\) for which
$$\frac { \mathrm { d } ^ { 2 } y } { \mathrm {~d} x ^ { 2 } } < 0$$
- State the geometrical interpretation of your answer to part (a), in terms of the shape of the graph of \(y = \mathrm { f } ( x )\) (not the gradient of the graph).