Energy Consumption—Strategic Oil Reserve: Throughout recent U.S. history, the U.S. Department of Energy has periodically released oil in its strategic oil reserves to help ease gasoline prices. In August 2011, the release had negligible effect on gas prices. “Although it helped initially to pull down prices it was probably too little,” said American Automobile Administration spokesman John Townsend. (Source: The Washington Times.) The amount of oil in the U.S. strategic oil reserve from 1980 to 2011 can be modeled by the function
f(x) = 0.1x3 − 5.24x2 + 88.1x + 128 0 ≤ x ≤ 31
where x represents the number of years since 1980, and f(x) represents the amount of oil in reserve in millions of barrels. (Source: U.S. Energy Information Administration.)
(a) Determine f′(x).
(b) How fast was the strategic oil reserve increasing in 1984?
(c) Evaluate f′(20) and interpret the result.
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