Find the minimum/maximum value of f(x) = 300/(1+2^(4-x)).

Question

jennychan12 · Answer

i know you take the derivative but i can't seem to get it.
$$f'(x) = \frac{ 300 \ln x (2^{4-x})} { (1+2^{4-x})^2 }$$
the derivative is correct?

jennychan12 · Answer

oh shoot. that lnx should have been a 2.
then you would just set the derivative equal to 0
so $$2^{4-x} = 0$$
but how solve for x?

jennychan12 · Answer

i meant lnx should have been ln 2

anonymous · Answer

There is no max or min. The function is asymptotically zero as x approaches - infinity and is unbounded otherwise.

whpalmer4 · Answer

Are you sure you have the problem right?  I don't see why it would have a maximum or a minimum

jennychan12 · Answer

my teacher copies everything from websites.
so yeah, the question is right.

anonymous · Answer

Righttttt. Because everything in the internet is right ;) There is no min or max then. (This is right.) As I said, the function is asymptotically zero (this does NOT mean the min is zero) as x approaches negative infinity. As x approaches infinity, the function becomes unbounded thus there is no absolute max.

Remember that by definition, a global max of a function is a point. Infinity is not a point.

jennychan12 · Answer

no. she just copied the problem, not the answer. she has the answer but she's not giving it to us.
-_-
I think my teacher might have made a typing error or something? 
Well, she did something wrong...

anonymous · Answer

Also, the reason is the same for a global min. It is also a point. You say but it approaches 0 as x approaches - infinity. True. But what POINT of the function--what SPECIFIC x value--is the function exactly equal to zero? There is none. Again, negative infinity is not a number. Thus, there is no absolute minima either. 
In short, the range of the function is bounded between (0,infinity) but it has no absolute min or absolute max.

whpalmer4 · Answer

All sorts of kids copying things onto OpenStudy manage to make mistakes, so there's an existence proof that even copying correct material can introduce error, and we have no evidence that the original was correct.  In any case, the derivative does have an interesting feature or two where one might find a minima or maxima.  You can probably guess where it will be looking at the original equation.