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. [-100,58]
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 [-100,58] that is a = -100 and b = 58
f(a) = f(-100) = (-4)*(-100) + 3 = 403
f(b) = f(58) = (-4)*58 + 3 = - 229
(f(b) - f(a)) / (b - a) = (f(58) - f(-100) / (58 - (-100)) = (- 229 - 403) / 158 = 632 / 158 = 4
The average rate of change of f(x)=-4x+3 over [-100,58] is 4.