Thread: [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

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 changes sign between and . But the drivative is continuous, and hence for some

CB

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

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