03/06/2013, 11:51 PM
picture this.
consider a C^2 function f(x) with
1) f(0) = 1 and f ' (0) > 1.
2) for x > 0 : f ' (x) > 0 and f '' (x) > 0.
3) f(1) = b and b > 2.
As b gets larger , what can you say about f(1,001) ?
Do you think f(1,001) is bounded as b grows or not ?
Once you solved this , notice how sexp_b(x) can be such a function if we set the conditions C^2 and 1) , 2) and 3).
Also notice that if we modify the conditions such that f ' (0) = 1 AND f '' (0) > 0 we get the same result.
( We do not get weird limits because of the property C^2 )
regards
tommy1729
consider a C^2 function f(x) with
1) f(0) = 1 and f ' (0) > 1.
2) for x > 0 : f ' (x) > 0 and f '' (x) > 0.
3) f(1) = b and b > 2.
As b gets larger , what can you say about f(1,001) ?
Do you think f(1,001) is bounded as b grows or not ?
Once you solved this , notice how sexp_b(x) can be such a function if we set the conditions C^2 and 1) , 2) and 3).
Also notice that if we modify the conditions such that f ' (0) = 1 AND f '' (0) > 0 we get the same result.
( We do not get weird limits because of the property C^2 )
regards
tommy1729
