need help with limits: f(x+y) = f(x)+f(y)-2xy, lim f(x)/h=7

[this guy]

here is the problem:

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 of f(x)/h=7 as h approaches zero

a. find f(0). Justify your answer.
i already did this section and and got f(0) = 0, which my teacher said was correct.

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

c. Find f(x)----- i know that this is the integral of b. but i don't know how to get b

plz help

 

[pka]

Re: need help with limits

\(\displaystyle \frac{{f(x + h) - f(x)}}{h} = \frac{{f(x) + f(h) - 2xh - f(x)}}{h} = \frac{{f(h)}}{h} - 2x,\quad h \ne 0\quad\)

 

[this guy]

Re: need help with limits

is this the derivative of the function, or do i still need to do something with it? i'm sry, i'm really slow at limits

 

[pka]

Re: need help with limits

To find the derivative you must finish the problem.
\(\displaystyle \lim _{h \to 0} \left[ {\frac{{f(h)}}{h} - 2x} \right] = ?\)

 

[this guy]

Re: need help with limits

i still am completely lost because we didn't do any examples of this in class... do i substitute in 0 for x? but then i'd still be left with the h on the bottom... wow i'm really confused

 

[pka]

Re: need help with limits

What does the given tell you about \(\displaystyle \lim _{h \to 0} \left[ {\frac{{f(h)}}{h}} \right]\)?

 

[this guy]

Re: need help with limits

it says f(x)/h =7 though, not f(h)/h

 

[pka]

Re: need help with limits

Go have good face-to-face talk with your instructor.
It appears that you need some fundamental help in functions.

 

[this guy]

Re: need help with limits

i've tried that, but she's one of those teachers who is amazingly smart, but can't teach to save her life. and since i wnet from a regular precalc class last year to an honors calc this year, i never had an introduction to limits. and this is the only thing that i am bad at in the class

 

[Deleted member 4993]

Re: need help with limits

Understanding limits is very important for calculus - do not cheat yourself!!

Sit down with her and figure out what you are missing in your understanding.

 

[Dr. Flim-Flam]

Is that f(x)/h = 7 or f(h)/h = 7 as h approaches 0?