# Thread: [SOLVED] constant infiniti function

1. ## [SOLVED] constant infiniti function

hey guys,have a tough problem....any help would be great

Let f(x) be C∞ function and assume that ∃a > 0 such that such that f ′(a) f '(2a) < 0. Show that f(x) has a local extrema on (0,∞).

f ' meaning f prime

2. Originally Posted by lsanger
hey guys,have a tough problem....any help would be great

Let f(x) be C∞ function and assume that ∃a > 0 such that such that f ′(a) f '(2a) < 0. Show that f(x) has a local extrema on (0,∞).

f ' meaning f prime
The derivative of $f$ changes sign between $a$ and $2a$. But the drivative is continuous, and hence $f'(x)=0$ for some $x \in (a,2a)$

CB

3. By the way, you titled this "constant infinity function".

You understand, do you not, that the "C" in $C^\infty$ means continuous, not "constant". Functions in $C^\infty$ are the functions, all of whose derivatives are continuous.