Question
Let f(t)=(1)/(t)
Find a value of t such that the average rate of change of f(t) from 1 to t equals 14.
t= ____
Find a value of t such that the average rate of change of f(t) from 1 to t equals 14.
t= ____
Answers
Reiny
f(t) = 1/t
f(1) = 1
( 1/t - 1)/(t-1) = 14 , where t ≠ 1
1/t - 1 = 14t - 14
times t
1 - t = 14t^2 - 14t
14t^2 - 13t - 1 = 0
(14t + 1)(t - 1) = 0
t = -1/14
f(1) = 1
( 1/t - 1)/(t-1) = 14 , where t ≠ 1
1/t - 1 = 14t - 14
times t
1 - t = 14t^2 - 14t
14t^2 - 13t - 1 = 0
(14t + 1)(t - 1) = 0
t = -1/14