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