Question 40251This question is from textbook College Algebra
: f(x)=x^2-2x
a) Find the average rate of change of f from 1 to x.
f(x) - f(1)
--------- (x does not = 1)
x - 1
b) Use result from part (a) to compute the average rate of change from x = 1 to x = 2.
c) Find an equation of the secant line containing (1, f(1)) and (2, f(2))
This question is from textbook College Algebra
Answer by venugopalramana(3286)   (Show Source):
You can put this solution on YOUR website! f(x)=x^2-2x
a) Find the average rate of change of f from 1 to x.
f(x) - f(1)
--------- (x does not = 1)
x - 1
AVG R.O.C.={(X^2-2X)-(1^2-2*1)}/(X-1)=(X^2-2X+1)/(X-1)=(X-1)^2/(X-1)...SINCE X IS NOT EQUAL TO 1,WE CAN DIVIDE WITH X-1 TO GET
R.O.C.=(X-1)
b) Use result from part (a) to compute the average rate of change from x = 1 to x = 2.
R.O.C.AT X=2....
2-1=1
c) Find an equation of the secant line containing (1, f(1)) and (2, f(2))
EQN IS
(Y-F(1)}/{F(2)-F(1)}={(X-1)/(2-1)}
F(1)=1^2-2*1=-1
F(2)=2^2-2*2=0
SUBSTITUTING
(Y+1)/1=(X-1)/(2-1)=X-1
Y+1=X-1
Y=X-2
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