United States electrical energy production (in trillions of kilowatt-hours) in year t (with 1900 corresponding to t = 0) is given by f (t), where f and its derivatives are graphed in Figs. 5(a) and 5(b).

(a) How much electrical energy was produced in 1950?

(b) How fast was energy production rising in 1950?

(c) When did energy production reach 3000 trillion kilowatthours?

(d) When was the level of energy production rising at the rate of 10 trillion kilowatt-hours per year?

(e) When was energy production growing at the greatest rate? What was the level of production at that time?

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2800 2400 2000 1600 1200 800 400 y 0 (1900) HI y = f(t) 10 20 30 40 50 60 70 80 90 (a) Figure 5 U.S. electrical energy production. t 70 60 50 40 30 20 y 10 y = f(t) A y=f"(t) 0 10 20 30 40 50 60 70 80 90 (1900) (b) t