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Unformatted text preview: MAC 2311 Test Three Review Answers, Fall 2011 1. (a) f ( x ) = (6 x ¡ 2) 3 ( x + 4) 2 ‡ 9 3 x ¡ 1 + 2 x + 4 · (b) f ( x ) = e x ¡ 3 3 p 6 + 3 x (3 x + 1) 2 ¢ ‡ 1 + 1 6 + 3 x ¡ 6 3 x + 1 · (c) dy dx = [ x + 4 + (ln x )(2 x + 4)] ¢ x x 2 +4 x (d) f ( x ) = • x cos x 1 + sin x + ln(1 + sin x ) ‚ (1 + sin x ) x ; m = ¡ … 2. a) 1 b) 2 c) ¡1 d) 1 2 e) e 2 =… f) 0 3. (a) t = 1 second, t = 4 seconds (b) (0 ; 1) and t > 4 seconds (c) displacement: ¡ 16 feet; total distance: 38 feet (d) speeding up: (1 ; 5 2 ) and t > 4; slowing down: (0 ; 1), ( 5 2 ; 4) 4. a) Marginal revenue: Revenue is increasing by \$15/unit; Production increases by 30 units/ week b) CORRECTION: Approximate the change in revenue as demand ( x ) decreases from 1600 to 1590 units. Approximate change: dR = ¡ 150 or a \$150 decrease in revenue; actual change ¢ R = R (1590) ¡ R (1600) = ¡ 150 : 47 5. The angle of elevation is decreasing by 1 rad/min....
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