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.

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.

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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) (Show Source): You can put this solution on YOUR website!

So then,

Compare this to a linear equation,

So then,

and

So f(x) is a linear function.
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