find 2 numbers whose sum is 12 and whose product is the maximum possible value. (hint: let x be one number, then 12-x the other number. Form a quadratic function by multiplying them and then find the maximum value of the function

Question

science0229 · Answer

Can you use a graphing calculator, or is this by hand?

science0229 · Answer

If you're doing this by hand, as the hint states, create a quadratic, which is y=x(12-x).

anonymous · Answer

does not specifically say, i guess i can use both, but don't know how

science0229 · Answer

Ok.

science0229 · Answer

Did you learn Calculus 1?

anonymous · Answer

no, i jumped from math 095 to math 103, all this is new to me... thanks for the help

science0229 · Answer

Ok. Then, let's do it the graphing calculator way.

anonymous · Answer

Isn't the answer just 6 for both numbers?

science0229 · Answer

Yes...

anonymous · Answer

both numbers

science0229 · Answer

Basically, x=6

science0229 · Answer

Do you know how, though?

anonymous · Answer

well, actually, i'm trying to figure it out and got 6 and -6 not sure if that's right... how did you get just 6

science0229 · Answer

Do you have a graphing calculator right now?

anonymous · Answer

oh wait, did you just pick 6 because it asks for the MAXIMUM value of the function

anonymous · Answer

yes i do

science0229 · Answer

Yes to your first question.
If you want to verify it, follow the steps.


1. Graph y=x(12-x)
2. Set your window as the following; domain=from 0 to 12, range=from -10 to 40
3. You should see a vertex, which is your maximum point.
4. Press 2nd+Trace, and press maximum.
5. Set your lower bound and upper bound, so that the vertex is in between.
6. The x-coordinate of the vertex is your x-value that makes the biggest possible product.

science0229 · Answer

That is if you have ti-83 or ti-84

anonymous · Answer

yes ti-84

science0229 · Answer

Then, follow the steps to get x=6.

anonymous · Answer

sorry, don't know how to figure it out on calculator either

anonymous · Answer

$$
y=x(12-x)= -x^2+12 x = -x^2 +12 x -36 +36= -(x-6)^2+36
$$

This a parabola of vertex (6,36} turning down. 
The maximum is when both numbers are equal to 6.
 6+6 =12 
6 x 6 =36

anonymous · Answer

where did you get the 36?

anonymous · Answer

just to complete the square.

anonymous · Answer

I added 36 and subtracted 36 so I added 0

anonymous · Answer

Have you studied parabolas?

anonymous · Answer

yes i have, a little confused about it, i but i think i got it

anonymous · Answer

Good

anonymous · Answer

thank you

anonymous · Answer

YW