# Derivatives and limits

1. Mar 9, 2008

### feuerwasser

1. The problem statement, all variables and given/known data

for all numbers x and y, let f be a function such that f(x+y)=f(x)+f(y)-2xy and such that the limit f(x)/h=7
h$$\rightarrow$$0

b. Use the definition of the derivative to find the derivative of f(x)

c. Find f(x)

i already did section a and and got f(0) = 0, which my teacher said was correct. and i know that to get section c i would just take the integral of b. but i have absolutely no clue how to get b. would i just take the derivative of f(x+y)=f(x)+f(y)-2xy and set f(x+y) to 0? or do i take the derivative of

2. Mar 9, 2008

### HallsofIvy

Staff Emeritus
The problem specifically says "use the definition of the derivative" which is, of course,
$$\lim_{h\rightarrow 0} \frac{f(x+ h)- f(x)}{h}$$
You are told that f(x+y)= f(x)+ f(y)- 2xy so f(x+h)= f(x)+ f(h)- 2xh.
[tex]\frac{f(x+h)- f(x)}{h}= \frac{f(h)- 2h}{h}= \frac{f(h)}{h}- 2[tex]
What is the limit of that?

3. Mar 9, 2008

### feuerwasser

would the limit be as h approaches zero, since that would cause it to be undefined? my teacher really didn't explain how to do limits so i'm kinda lost