Thoroughly investigate the graph of $y = e^{x}\cos\left(x\right)$ over the interval $[–1, 5]$. Identify all of the important qualities, such as where the function is increasing, decreasing, concave up, and concave down. Also identify point(s) of inflection and intercepts and provide the graphs of $y = f ′\left(x\right)$ and $y = f^{\prime\prime}(x)$. Be sure to justify all statements both graphically and analytically.