Engineering—Nuclear Power Generation: Since the first commercial nuclear power plant was constructed in the United Kingdom in 1953, nuclear power has been a promising and sometimes controversial method to supply the public’s electric needs. The annual amount of power generation from nuclear sources from 1990 to 2010 in the United States can be modeled by the function
f(x) = −0.55x 2 + 22.57x + 575.87 0 ≤ x ≤ 20
where x represents the number of years since 1990, and f(x) represents the amount of power generation from nuclear 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).
(b) Evaluate and interpret f′(15).
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