SOLUTION: 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 -113

Question 212469: 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 -113

Answer by RAY100(1637) (Show Source): You can put this solution on YOUR website!
f(t) = 1/t
.
f(1) = 1/1 =1,,,,,,,(1,1)
.
f(t) = 1/t,,,,,,,,,,,(t,1/t)
.
rate of change is slope = (y2-y1)/(x2-x1) = {(1/t) -1}/ {t-1) = {(1-t)/t}/{t-1)= {(-1)(t-1)/t} /{t-1} = -1/t
.
m(-113) = -1/(-113) = + 1/113
.
check:,,,,,f(1) =1,,,,(1,1)
.
f(-113)= -1/113,,,,,,,(-113, -1/113)
.
m= {1-(-1/113)}/ {1-(-113)}= {1+1/113}/ {1+113)= {(113+1)/113} /(1+113) = 1/113,,ok
.

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