Question: (a) Sketch the graph of \({{x}^{3}}-6{{x}^{2}}+9x+6\). Show explicitly where the function is increasing or decreasing. Label points that correspond to local extrema

(b) Use the results in part (a) to prove that the equation \({{x}^{3}}-6{{x}^{2}}+9x+6=0\) has only one real solution. Determine two consecutive integers n and n + 1 in such a way that the solution is between these integers