<p>Suppose f is a function for which lim x-->2 f(x)-f(2)/x-2 = 0. Which MUST be true, MIGHT be true, or are NEVER true?</p>
<p>a. derv. of 2 is 2. I know that's never
b. f (2)= 0
c. lim x-->2 f(x)=f (2)
d. f(x) is continuous at x=0
e. " x=2</p>
<p>for b-e, I think it's might,might,might,must but can someone help with those real quick.</p>
<p>Also</p>
<p>f(x+y)=f(x)+f(y)+2xy and lim h-->0 f(h)/h=7</p>
<p>Find derv. of f(x)</p>
<p>No clue where to even start.</p>
<p>Please aid me with these 2.</p>
<p>anyone who is a calculatory genius please? helping me will earn you a title in the Logistical Regime as Logistical Einstein</p>
<p>Okay, so basically the limit that they gave you was a fancy way of telling you the derivative.
That is: f ' (x) = lim as x-->a of f(x) - f (a) (all over x-a)</p>
<p>So, if f ' (x) = 0 then:
A. Never (the derivative at x=2 is 0, not 2)
B. Maybe (f(2) could equal 2, if the function intersects x axis at x=2 but will not if the function is doesn't intersect there...since you can't determine the function from the information given, it is maybe)
C. Maybe (this would be true if the function is continuous and contains the point (2,2))
D. Maybe (to determine this you would have to the continuity at that point, you would have to see if the limit as x approaches 0 from the left equals the limit as x approaches 0 from the right...since you don't have that information you can't be sure...it's a maybe)
E. Must (that one is pretty self-explanatory)</p>
<p>thank you logistical einstein. do we have a logistical newton to help me with my other question?</p>
<p>I'm not sure I understand the second part...Was there more to the question?</p>
<p>The questions in full:</p>
<p>Let f be a function which satisfies f(x+y)=f(x)+f(y)+2xy for all real numbers x and y and suppose lim h-->0 f(h)/h=7.</p>
<p>a. Find f(0). The teacher gave the answer because we bugged him. It's 0.</p>
<p>b. Use the definition of the derivative to find f '(x).</p>
<p>Never mind, I think they probably want you to use the definition of the derivative to find it.
So lim at h-->0 of f(x+h) - f(x)/ h:
f(x+h) = (x+h)^2 = x^2 + h^2 + 2xh
f (x) = x^2</p>
<p>So, the lim at h--> of h(h+2x) / h= lim as h-->0 of h+2x=(0)+2x=2x</p>
<p>Wow, I have no idea with that one...I just plugged the answer into the definition of a derivative but I didn't realize it's related to that second part about the lim h -->0...Good luck!</p>