Engineering—Natural Gas Power Generation: Russia and the United States are the two leading...

Engineering—Natural Gas Power Generation: Russia and the United States are the two leading countries in natural gas production, and natural gas accounts for 23.4% of the total U.S. electricity production. The annual amount of power generation from natural gas sources from 1990 to 2010 in the United States can be modeled by the function

 f(x) = 0.67x2 + 16.63x + 373.13 0 ≤ x ≤ 20

where x represents the number of years since 1990, and f(x) represents the amount of power generation from natural gas power plants, measured in billions of kilowatt hours (BkWh). (Source: U.S. Energy Information Administration.)

(a) Use the definition of derivative to determine f′(x).

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(b) Evaluate and interpret f′(8).