Problema Solution
Let f be the linear function defined by f(x)=-4x+3. Find the average rate of change in f over the following intervals [1.8,20.1]
Answer provided by our tutors
The average rate of change of f over [a, b] is defined by (f(b) - f(a)) / (b - a)
f(x)=-4x+3 and the interval is [1.8,20.1] that is a = 1.8 and b = 20.1
f(a) = f(1.8) = (-4)*1.8 + 3 = - 4.2
f(b) = f(20.1) = (-4)*20.1 + 3 = - 77.4
(f(b) - f(a)) / (b - a) = (- 77.4 - (-4.2)) / (20.1 - 1.8) = - 73.2 / 18.3 = 4
The average rate of change of f(x)=-4x+3 over [1.8,20.1] is 4.