We were given a problem:(adsbygoogle = window.adsbygoogle || []).push({});

"The slope of f(x) at point x is twice the x value. f(2) = 3. Find f(3)."

I did this the conventional way:

f(x) = [tex]\int[/tex] 2x dx

= x^2 + c

Solving with the initial condition of f(2) = 3 gives me f(x) = x^2 - 1. So f(3) = 8.

My class did it a different way. They found f'(3) and f'(2), took the average and added that to the initial value 3, to get eight.

So can someone prove:

(f'(b)+f'(a))/2+f(a) = f(b) given |b-a| = 1 ?

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# Homework Help: Puzzling solution

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