# Finding locations of absolute extrema

• Feb 4th 2007, 12:15 PM
Mathamateur
Finding locations of absolute extrema
Trying to review for my test next week and this is an example problem that I have a feeling will be on the test yet I am somewhat lost on how to solve. Thanks in advance for the help!

Find the locations of all absolute extrema for the function....

f(x) = 2x^3 + 3x^2 -36x +12 with the domain [ -2, 4 ]

I know I'm supposed to use the first derivative test correct?

f'(x) = 6x^2 + 6x - 36
0 = 6x^2 + 6x - 36

Could someone please solve it from here(assuming I am right so far)?
• Feb 4th 2007, 12:40 PM
topsquark
Quote:

Originally Posted by Mathamateur
Trying to review for my test next week and this is an example problem that I have a feeling will be on the test yet I am somewhat lost on how to solve. Thanks in advance for the help!

Find the locations of all absolute extrema for the function....

f(x) = 2x^3 + 3x^2 -36x +12 with the domain [ -2, 4 ]

I know I'm supposed to use the first derivative test correct?

f'(x) = 6x^2 + 6x - 36
0 = 6x^2 + 6x - 36

Could someone please solve it from here(assuming I am right so far)?

Three points:
1) You are looking for "relative" extrema within the interval. This function has no absolute extrema.

2) Don't forget the end points of the domain!

3) Dude! :confused: This is a quadratic. If you can't figure out how to solve it, just use the quadratic formula. So saying:
$6x^2 + 6x - 36 = 0$

$6(x^2 + x - 6) = 0$

$x^2 + x - 6 = 0$

$(x + 3)(x - 2) = 0$

So x = 2 or -3.

-Dan
• Feb 5th 2007, 10:00 AM
Mathamateur
It says specifiacally to look for any "absolute" extrema though.

So should I plug both of those numbers back into the original to find where they are maximums and minumums. Should I also plug the 2 numbers in the domain in? If so, how do I know when they are "absolute" extrema?

If someone could show me how to do this I would be very thankful.
• Feb 5th 2007, 10:15 AM
CaptainBlack
Quote:

Originally Posted by Mathamateur
It says specifiacally to look for any "absolute" extrema though.

So should I plug both of those numbers back into the original to find where they are maximums and minumums. Should I also plug the 2 numbers in the domain in? If so, how do I know when they are "absolute" extrema?

If someone could show me how to do this I would be very thankful.

Poor use of language it means find the global extrema in [-2, 4].

Topsquark has forun the relative extrema of f(x) occur at x=2, -3. Now -3
is not in the interval so is not what we want.

Hence the global maximum in [-2,4] occurs at one of the points x=-2, x=2 or x=4, and the global minimum is also at one of these.

Now f(x) takes values 80, -32, 44 at these points, so the global maximum is 80, and the global minimum is -32.

RonL
• Feb 5th 2007, 10:25 AM
Mathamateur
thank you so much, perfectly explained what I was confused on.