Women’s Studies—Unmarried Labor Force: A sociological topic that has been discussed since...

Women’s Studies—Unmarried Labor Force: A sociological topic that has been discussed since the end of World War II is the status of women in the labor force. The number of unmarried women in the U.S. labor force from 1970 to 2010 can be modeled by

 f(x) = 1.11(1.57x + 17.27)0.66 0 ≤ x ≤ 40

where x represents the number of years since 1970 and f(x) represents the number of unmarried women in the U.S. labor force, measured in millions. (Source: U.S. Bureau of Labor Statistics.)

(a) Determine f′( x).

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(b) Evaluate f(35) and f′(35) and interpret each.