Be who you needed when you were younger. Anonymous
Idea Transcript
AVERAGE RATE OF CHANGE vs AVERAGE VALUE Left side is the slope between two points … Right side is the average value of f ' ( x )
Average Rate of Change in f (x) = Average Rate of Change in f (x) f (b ) - f ( a ) b-a
b
=
ò
f ' ( x ) dx
a
b-a f ( x) a b
b-a f (b ) - f ( a ) b-a
An Example … Find the average acceleration from t = 9 to t = 15 seconds. Method 1: Average acceleration = Average rate of change in velocity = Slope between two points on velocity function v (15) - v (9)
15 - 9
Method 2: Average acceleration = Average value of acceleration function = “Integral” (of acceleration) over “interval” 15