9i gave that exp for prophet to check . so cut short certain detailed exp u shud see prophets exp in the link he gave thats more mathematical
THIS ONE IS FRM DA FORUM ITSELF :
If f(x) f'(x) f"(x)>0 for all x in R, prove that f(x) is a strictly increasing function
CAN NE1 PLZZZ XPLAIN ME THIS EXPLANATION OF CELESTINE
f'x never 0 , so either strict inc or strict dec
if strict dec , wen fx bcom -ve , f"x +ve , inc f'x , inc fx so at some pt , theres a minima at fx so f'x =0 contradicting
wen fx +ve , f"x -ve
if strict inc , wen fx bcom -ve , f"x -ve , f'x red , fx further reduce so no constraint
wen fx +ve , f"x +ve similar reason
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10 Answers
9
21i saw that link provided by prophet,
but found it a little toooo long. I found ur meth more logical n concept-based. But jus couldnt figure out da last part.
It wud be gr8 if u cud tell me how did u draw the conclusions???
1if strict dec , wen fx bcom -ve , f"x +ve , inc f'x , inc fx so at some pt , theres a minima at fx so f'x =0 contradicting
wen fx +ve , f"x -ve
if strict inc , wen fx bcom -ve , f"x -ve , f'x red , fx further reduce so no constraint
wen fx +ve , f"x +ve similar reason
can u plz explain dis part
9u try drawing a curve
ull find that f f' and f" must always be of same sign or else theyll pass thru 0
i think i skipped this imp exp
21OH K COOOLLLL..........
NICE GENERALISATION MAN!!!!!!!
AND HEY BY THE WAY " theyll pass thru 0" means all three of them or jus f'(x)???
This is jus for my knowledge, as ther wud b a contradictn frm the given statement even if ne1 one ofthem was 0......
21" ull find that f f' and f" must always be of same sign or else theyll pass thru 0"
SO U MEAN TO SAY DAT NE KE WEN ANY 2 OUT OF f, f' & f'' are of opp sign theyll pass thru 0"
so wat exactly is = "THEY" is wat i wanted to know....
9i said f f' f'' cant be 0
so being a continuous function they need to maintain the same sign throughout