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Given a function f(x), I'm wondering if the slope of the secant between points a, f(a) and b, f(b) is equal to the average of the derivative at a and b.
Mathematically, I want to know whether:
[itex]\frac{f(a) - f(b)}{a - b}[/itex] = [itex]\frac{f'(a) + f'(b)}{2}[/itex]
is true. I can see that it is for polynomial functions, but I can't seem to prove this relationship for a general function, f(x).
This isn't homework, I'm just curious. Thanks for the help!
Mathematically, I want to know whether:
[itex]\frac{f(a) - f(b)}{a - b}[/itex] = [itex]\frac{f'(a) + f'(b)}{2}[/itex]
is true. I can see that it is for polynomial functions, but I can't seem to prove this relationship for a general function, f(x).
This isn't homework, I'm just curious. Thanks for the help!