Question: Given \(f\left( x \right)={{x}^{3}}-12{{x}^{2}}+36x+5\), on \(\left( -\infty ,\infty \right)\)

(a) Find the critical numbers of the first-order

(b) Find the intervals of increase and decrease. Show work that supports conclusion

(c) Give the coordinates of the local maximum, if any

(d) Give the coordinates of the local minimum, if any

(e) Find the intervals on which f(x) is concave up and the intervals on which it is concave down. Show the work. Find the coordinates of the inflection point, if there is any