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zab505 · Answer

attachment

zab505 · Answer

@Hero

hero · Answer

Have you graphed them yet?

zab505 · Answer

yes

hero · Answer

So which choice do you believe is correct and why?

zab505 · Answer

d is a def but I'm not sure of A

hero · Answer

Does f(x) have a max value? If so what is it?

zab505 · Answer

2

hero · Answer

When it comes to problems like these, it is important to discern what you know from what you don't know.

hero · Answer

You must ask yourself, "Does f(x) have a max value?". Just because a function is approaching what appears to be a max value, doesn't mean that a max value exists.

hero · Answer

Here's the way to figure out if f(x) has a max value of 2.
f(x) = $-5^x + 2$

Let f(x) = 2

2 = $-5^x + 2$

Now try to solve for $x$

If you are able to solve for $x$, then the max of f(x) is 2. If not, then 2 is not the max. Try it.

zab505 · Answer

=0

hero · Answer

Can you show the work you've done for this? If the max value of f(x) is 2, then there has to be a corresponding value of x, otherwise, 2 is not the max. Notice that f(x) "approaches" 2 as x gets smaller and smaller. To observe this, you have to zoom in on the graph of f(x). But the way to know for sure is to attempt to solve for x when f(x) = 2.

zab505 · Answer

Ah so A and d only

hero · Answer

1. The max value of a function doesn't exist if it is only approaching the assumed max value. In other words, we cannot even describe 2 as a "max value" if f(x) = 2 doesn't exist. 

2. If f(x) = 2 doesn't exist, but g(x) = 2 does and 2 is the max of g(x), then f(x) and g(x) can't possibly have equivalent max values.

hero · Answer

The logic of reasoning is this:

1. Does f(x) = 2 exist? NO
2. Does f(x) have a max value? NO. 

Therefore, any such sentence that suggests or hints at a max value for f(x) is false. (there's no such thing as a function approaching a max value if the max value doesn't exist).

zab505 · Answer

So the what would be the answer

hero · Answer

Start asking yourself questions about g(x).

zab505 · Answer

there is only one with g(x)

hero · Answer

Try to understand the difference between f(x) and g(x) with regard to a max value before selecting a choice.

zab505 · Answer

so only A?

hero · Answer

Here's an idea...Describe in words what you understand as far as the difference between f(x) and g(x) and post it here.

zab505 · Answer

Can you help me?

hero · Answer

@zab505, I can only help you so much. At some point, you must be able to think for yourself. At least make an attempt at describing the differences between f(x) and g(x).

hero · Answer

Start off by answering a couple questions:
What kind of function is f(x)? 
What kind of function is g(x)?

anonymous · Answer

A plot and solution using Mathematica is attached.

hero · Answer

@robtobey, since when does "limit" become synonymous with "max value"? Without guidance, explanations, and insight, your solution is not helpful.

hero · Answer

http://www.wolframalpha.com/input/?i=max+value+of+-5%5Ex+%2B+2

anonymous · Answer

Within the plot's field of view, one cannot guess how high -5 x^2  + 2 will rise.
The derivative of -5 x^2  + 2 , -10x, is useless to answer the above concern.
From my point of view the limit approach solves the problem.

hero · Answer

@robtobey, let f(x) = 2, then attempt to solve for x.

hero · Answer

2 can't be the max value of f(x) if there's no corresponding x value.

anonymous · Answer

It's been many decades since I was a student, but is not the case that the calculus is based on a limit process?

hero · Answer

You assume that calculus was necessary for this. It is not.

zab505 · Answer

Thank you both very much!