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Homework Statement
For all real numbers x and y, let f be a function such that f(x+y)=f(x)+f(y)+2xy and such that the limit as h approaches zero is f(h)/h=7. [tex]\stackrel{Lim}{h\rightarrow0}\frac{f(h)}{h} = 7[/tex]
a) Find f(0) and justify your answer.
b) Use the definition of the derivative to find f ' (x).
c) Find f(x).
NO CALCULATOR USE ALLOWED!
Homework Equations
Limit as h->0 is (f(x+h)-f(x))/h
The Attempt at a Solution
To solve part a, I looked at the original equation. To find f(0), I just put in 0 for x and 0 for y.
Let x=y=0.
And thus, I got f(0)=0, so now part a should be cleared. Right?
Then I get to part b and I'm a little stuck. Find f ' (x) ? Should I be using the equation I put in the relevant equations section to help me out with this?
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