Posted by Jenn on Friday, March 15, 2013 at 11:28am.
Determine without graphing, whether the given function has a maximum value and then find the value. f(x)=3x^2+30x1

Determine without graphing  Reiny, Friday, March 15, 2013 at 11:42am
Steve had already answered this question for you.
http://www.jiskha.com/display.cgi?id=1363360907
What part of his answer did you not like ?

Determine without graphing  Jenn, Friday, March 15, 2013 at 11:44am
I needed help learning how to find the value.

Determine without graphing  drwls, Friday, March 15, 2013 at 11:52am
f(x) = 3(x^2 + 10x +25)76
= 3(x+5)^2 76
The function has no maximum. It has a minimum of 76 when x = 5.

Determine without graphing  Steve, Friday, March 15, 2013 at 11:57am
Hmmm. I explained that there is no maximum value. Don't expect to be able to find it.
Now, if you want to find the minimum value, try completing the square:
3x^2+30x1
= 3(x^2 + 10x)  1
= 3(x^2 + 10x + 25)  1  75
That step is the key. We added 75 to complete the square, so we have to subtract it as well to avoid changing f(x)
= 3(x+5)^2  76
Now you can see that since (x+5)^2 is always at least zero (since squares are never negative), the smallest value for (x+5)^2 is when x = 5. In that case, f(x) = 3(0)  76
So, f(5) = 76, and it can never be less than that, because whatever x is, (x+5)^2 will be some positive number, making f(x) > 76
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