Recent content by antibody

i m not sure if my answer is completed,, can anyone check it for me? thx! suppose f''(x)<4 for all x in [0, 1/2]，apply mean value theorem,if0<=x<=1/2 (f'(x)-f'(0))/(x-0)<4 ==> f'(x)<4x,one more time mean value theorem,if0<=x<=1/2 (f(x)-f(0))/(x-0)<4x ==>f(x)<4x^2 f(1/2)<1 suppose f''(x)>-4...

it will probably be a test question on the test tmr... using contradition? or not..i don't have enough time to think about it now, just want to see some clues.

neeeeed helppppp for a question,,urgent!(not hw) Hi, I have been working on this question for some time,, but still couldn't solve it,,does anyone have an idea? thanks for helping! Prove that if f is a twice differentiable function with f(0)=0 and f(1)=1 and f '(0)=f '(1)=0, then / f ' ' (x)...

and same thing happens to quesntion no.3 ... if the question gives me some precise function, i probably can solve it, but this one i am still working on it, my idea is x^n when x>=0 f(x)= 0 when x<=0 so the f ' (x) = n x^(n-1) when x>0 and f ' (x)=0 when x<0 then...

for the second one , i know how to prove the converse, like let B>1, if f satisfies /f(x)/ <=/x/^B, prove that f is differentiable at 0, this one will be easier, first let x=0 then f(0)=0, and i know to prove some fn is differentiable at some point x, it means to prove lim(h->0) f(x+h)-f(x)...

1. Suppose that f(a)=g(a) and the left-hand derivative of f at a equals the right-hand derivative of g at a. Define h(x)=f(x) for x<=a, and h(x)=g(x) for x>=a. Prove that h is differentiable at a. 2. Let 0<B<1. Prove that if f satisfies /f(x)/ >= /x/^B and f(0)=0, then f is not differentiable...

so confused,,,some ppl say it does, some ppl say it does not .. anyone can give a conclusion?

o i have an ans here, but don't know whether,, let's see It seems like you should not, because D = lim(x->a) f'(x) {Given} = lim(x->a) lim(y->x) (f(y)-f(x))/(y-x) {Definition of derivative} = lim(a+h->a) lim(a+h+g->a+h) (f(a+h+g)-f(a+h))/g {Substitution} = lim(h->0) lim(g->0)...

i think there's a problem with this ans since the limit does not exist if f(x)=(x+1)/(x+1)...hmm... i am not sure..

The professor said he didnt know the ans of this qn, so, can u help? Question: Can you have lim_x->a f '(x) = D , f ' (a) exists, but not equal to D? any one can give an example? thx!