Math 211 Business Calculus Applications of Derivatives

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Graphs with asymptotes Sketch the graph <strong>of</strong>y = f(x) = x−2 x+1 We need the derivatives By the quotient rule f ′ (x) = (1)(x+1)−(x−2)(1) (x+1) 2 = x+1−x+2 (x+1) 2 – p. 10/34
Graphs with asymptotes Sketch the graph <strong>of</strong>y = f(x) = x−2 x+1 We need the derivatives By the quotient rule f ′ (x) = (1)(x+1)−(x−2)(1) (x+1) 2 = x+1−x+2 (x+1) 2 3 = (x+1) 2 – p. 10/34
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- p. 1/34 Math 211 Business Calculu
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- p. 2/34 Asymptotes A nonvertical
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- p. 3/34 Example Lety = f(x) = x+
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Example Lety = f(x) = x+ 1 x f ′
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- p. 4/34 Graph of x+1/x ♣ (1,2)
Page 25 and 26: Graph of x+1/x 1 lim x→0 + x =
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Page 49 and 50: Horizontal Asymptotes To find horiz
Page 55 and 56: - p. 7/34 Computing Limits When fin
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Page 63 and 64: Example 1. Compute the limit x 2 +8
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Page 67 and 68: - p. 9/34 Second example This limit
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Page 71 and 72: - p. 9/34 Second example This limit
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Page 87 and 88: - p. 12/34 Find the Asymptotes For
Page 89 and 90: Find the Asymptotes For y = f(x) =
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- p. 17/34 Max versus Min R = −0.
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- p. 18/34 Maximize Revenue The rev
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- p. 19/34 Max versus Min R = x 3
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- p. 20/34 Maximize Profit As a gen
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- p. 21/34 Maximize Profit Example
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What level of sales maximizes profi
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- p. 22/34 Ticket Sales Problem •
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- p. 23/34 Ticket Sales Setup Letx=
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- p. 28/34 Another Fencing Problem
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Another Fencing Problem The owner o
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- p. 30/34 Fence Solution Solve xy
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Fence Solution Solve xy = 810 fory:
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- p. 32/34 Marginal Revenue, Profit
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- p. 33/34 Marginal Example Flying
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Math 211 Business Calculus Applications of Derivatives

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