Question: Union membership as a percentage of the total labor force can be modeled by the M(x), where \(M\left( x \right)=0.0002{{x}^{3}}-0.049{{x}^{2}}+3.75x-68\), where M(x) is the membership as a percentage of the labor force and x is the number of years after 1900.

(a) Determine the first derivative. Use the graph of the first derivative to determine the behavior of M(x).

(b) Determine the second derivative. Use the graph of the second derivative to determine the behavior of M(x).
(c) Determine the value of the derivative for 1950 and interpret it.
(d) Determine the value of the derivative for 1980 and interpret it.
(e) Determine the value of the derivative for 2007 and interpret it.
(f) Determine the value of the derivative for 2020 and interpret it.