SOLUTION: Suppose the function f has the same average rate of change C between any two points; then for the points a and x we have C= f(x)-f(a)/x-a. Show that f(x) is a linear function.

Algebra ->  Average -> SOLUTION: Suppose the function f has the same average rate of change C between any two points; then for the points a and x we have C= f(x)-f(a)/x-a. Show that f(x) is a linear function.       Log On


   

Question 946213: Suppose the function f has the same average rate of change C between any two points; then for the points a and x we have C= f(x)-f(a)/x-a. Show that f(x) is a linear function.
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
%28f%28x%29-f%28a%29%29%2F%28x-a%29=C
So then,
f%28x%29-f%28a%29=C%28x-a%29
f%28x%29=f%28a%29%2BCx-Ca
f%28x%29=Cx%2B%28f%28a%29-Ca%29
Compare this to a linear equation,
f%28x%29=mx%2Bb
So then,
m=C
and
b=f%28a%29-Ca
So f(x) is a linear function.