application on integration problem: f(1)=1, f(2)=10; given f(x+h)- f(x)=Kxh-2(h)^2...

[Mina]

If f(x) is a real function satisfies the following conditions : f(1)=1 , f(2)=10 . Given that : f(x+h) - f(x) =Kxh-2(h)^2 .how to find f(x) ?

 

[Harry_the_cat]

If f(x) is a real function satisfies the following conditions : f(1)=1 , f(2)=10 . Given that : f(x+h) - f(x) =Kxh-2(h)^2 .how to find f(x) ?

Remember that \(\displaystyle f '(x) = lim(h->0) \frac{f(x+h) - f(x)}{h}\)

So in your case:

\(\displaystyle f '(x) =lim(h->0)\frac{Kxh-2h^2}{h}\)

Continue to find \(\displaystyle f ' (x)\).

Integrate to find \(\displaystyle f(x)\). Don't forget c.

Use f(1)=1 , f(2)=10 to find c and K.