Derivatives and limits

  • #1

Homework Statement



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[tex]\rightarrow[/tex]0
a. find f(0). Justify your answer.


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
 

Answers and Replies

  • #2
HallsofIvy
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The problem specifically says "use the definition of the derivative" which is, of course,
[tex]\lim_{h\rightarrow 0} \frac{f(x+ h)- f(x)}{h}[/tex]
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
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
 

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