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

2. Concave up, Concave down, Increasing, 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) =
f(t) =
a) The values are decreasing, then the function is decreasing or falling Slope of the tangent line < 0
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 from 18 to 10: decreases by from 10 to 5: decreases by from 5 to 2: decreases by It decreases in slower and slower rate, then it is Concave Up
b) from 20 to 18: decreases by from 18 to 15: decreases by from 15 to 10: decreases by from 10 to 3: decreases by It decreases in faster and faster rate, then it is Concave Down
Concave up
m < 0 Negative Falling, Decreasing
m < 0 Negative Falling, Decreasing
Concave down

3. Linear Increase or Decrease Exponential Growth or Decay
f(t) t 1 2 3 4 6 8 10 12
Linear Increase y = mx + b m > 0
f(t) t 2 4 6 8 12 9 3
Linear Decrease y = mx + b m < 0
Or: y = 2x + 4 ; (m = 2)
Or: y = -1.5x ; (m = -1.5)
f(t) t 1 2 3 12
13.2
14.52
15.972
f(t) t 1 2 3 15 12
9.6
7.68
Exponential Growth P=P0(a)t a > 1
Exponential Decay P=P0(a)t a < 1
Or: P = 12(1.1)t ; (a = 1.1)
Or: P = 15(0.8)t ; (a = 0.8)