Math Is Fun Forum
  Discussion about math, puzzles, games and fun.   Useful symbols: √ ∞ ≠ ≤ ≥ ≈ ⇒ ∈ Δ θ ∴ ∑ ∫ π -




Not registered yet?

  • Index
  •  » Help Me !
  •  » Little derivative problem (prove or give a counterexample)

Post a reply

Go back

Write your message and submit
:) :| :( :D :o ;) :/ :P :lol: :mad: :rolleyes: :cool: | :dizzy :eek :kiss :roflol :rolleyes :shame :down :up :touched :sleep :wave :swear :tongue :what :faint :dunno

Go back

Topic review (newest first)

2013-01-17 07:02:59

However, we observe that the derivative (where it does exist) goes to zero... maybe moving (1) to the hypothesis... Anyway, that was a good example, thank you smile

2013-01-17 06:43:00

uhmm i'm trying to figure out how do you see that f goes to a y0... let's see:

so the c(n) part converges and the x part of course does. Is there a easiest way to see that?

2013-01-17 06:22:12

Not true. may only be piecewise differentiable, not wholly differentiable.

Let us define a sequence of functions as follows:

is chosen so that
for continuity. Then if we make
by piecing together the functions
and their domains, this function satisfies all your given conditions but is not differentiable at any integer value of
, where the gradient changes abruptly.

2013-01-17 05:49:29

Hi guys, i'm trying to figure out if this is true or not, can you help me?

Conjecture: Let f:[m,+∞)->R be a continuous and monotonous function with a horizontal asymptote y0 (as x->+∞). Then:
1) f is derivable.
2) f'->0 as x->∞.

I ask for f being monotonous because the only counterexamples, to the non-improved conjecture, that came to my mind are things like f(x)=sin(x^2)/x.

Thanks in advance.

Board footer

Powered by FluxBB