Question

Find two nonnegative numbers whose sum is 1 such that the sum of the square of one and twice the square of another is minimum

Answer 1

We need to translate the words into equations: we have
a + b = 1 and
a^2 + 2b^2 = M,
where a and b are the two nonnegative numbers we're looking for and M is the thing we want to minimize.

From here, we can solve the first equation for one variable, plug into the second, and then take the derivative of the second to find when M is minimized. Can you take it from here?

Answer 2

question-does the minimum mean you want it to equal the smallest thing possible?

Answer 3

Yep.

Answer 4

What i got was x^2 + 2(1-x)^2
ds= 2x+4(1-x)(-1) = 0

Answer 5

then im unsure of what to do next

Answer 6

so far I've 3a62-4a+2. I think we graph and find minimum there

Answer 7

Wo, I meant 3a^2, not the 62 thing

Answer 8

Wait, Peser, where are ur x's coming from?

Answer 9

Once you have
2x+4(1-x)(-1) = 0
solve for x!
2x-4+4x = 0
6x-4 = 0
6x = 4
x = 2/3.

Answer 10

:(