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Sections: 1.3 and 1.5 m > 0 Positive Rising, Increasing Concave up m > 0 Positive Rising, Increasing Concave down Use the following table to decide if the function is increasing, decreasing, concave up, concave down: f(t) = 3 5 10 18 30f(t) = 3 10 15 18 20 a) The values are increasing, then the function is increasing or rising. Slope of the tangent line > 0 b) from 3 to 5: increases by 2 from 5 to 10: increases by 5 from 10 to 18: increases by 8 from 18 to 30: increases by 12 It increases in faster and faster rate, then it is Concave Up a) The values are increasing, then the function is increasing or rising. Slope of the tangent line > 0 b) from 3 to 10: increases by 7 from 10 to 15: increases by 5 from 15 to 18: increases by 3 from 18 to 20: increases by 2 It increases in slower and slower rate, then it is Concave Down

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Concave up, Concave down, Increasing, Decreasing m < 0 Negative Falling, Decreasing Concave down Concave up m < 0 Negative Falling, Decreasing Use the following table to decide if the function is increasing, decreasing, concave up, concave down: (notice that the tables are the same as the previous example, but in reverse order) f(t) = 30 18 10 5 2f(t) = 20 18 15 10 3 a) The values are decreasing, then the function is decreasing or falling. Slope of the tangent line < 0 b) from 30 to 18: decreases by 12 from 18 to 10: decreases by 8 from 10 to 5: decreases by 5 from 5 to 2: decreases by 3 It decreases in slower and slower rate, then it is Concave Up a) The values are decreasing, then the function is decreasing or falling. Slope of the tangent line < 0 b) from 20 to 18: decreases by 2 from 18 to 15: decreases by 3 from 15 to 10: decreases by 5 from 10 to 3: decreases by 7 It decreases in faster and faster rate, then it is Concave Down

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Linear Increase or Decrease Exponential Growth or Decay Linear Increase y = mx + b m > 0 Or: y = 2x + 4 ; (m = 2) Linear Decrease y = mx + b m < 0 Exponential Growth P=P 0 (a) t a > 1 Exponential Decay P=P 0 (a) t a < 1 Or: P = 12(1.1) t ; (a = 1.1) Or: P = 15(0.8) t ; (a = 0.8) f(t)f(t) t 0123401234 4 6 8 10 12 f(t)f(t) t 0246802468 9 6 3 0 Or: y = -1.5x + 12 ; (m = -1.5) f(t)f(t) t 01230123 12 13.2 14.52 15.972 f(t)f(t) t 01230123 15 12 9.6 7.68

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20 19181716151413121110987654321 © S Haughton 2010 1 more than 3?

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