Question

If y=2x^2-8x, what is the minimum value of the product xy?

Answer 1

This is another problem from my practice AB exam I was given the other day that I don't quite remember how to do

Answer 2

set the derivative equal to 0

then find the second derivative to see if it's a min or a max

Answer 3

I thought the second derivative only tells you the concavity?

Answer 4

The second derivative is just y=4

Answer 5

you're right, scratch that second part

Answer 6

ok

Answer 7

The answer said that it was -8, but I am almost 100% sure that it is -16

Answer 8

Because I set the first derivative= to 0 and I got x=2

Answer 9

1 sec i'm checking with my roommate

Answer 10

Then I plugged that into the equation for y and I got -8

Answer 11

Ok thanks

Answer 12

Then I multiplied -2 by 8 to get the product of xy

Answer 13

okay so set derivative to 0....that's a critical point

if at that point the 2nd derivative is positive that means that the first derivative just switched from negative to positive, signaling a min

to find the y value plug the x value into the original equation

Answer 14

Yes. I got 8 for the y val

Answer 15

-8

Answer 16

So I multiplied 2 by -8 and got -16. My stupid packet is telling me that the answer is -8

Answer 17

I think that they forgot to multiply at the end tho

Answer 18

i'm pretty sure it's -8, why are you sure it needs to be -16?

2(2)^2 -8(2) = -8

Answer 19

That just gives you the y val

Answer 20

They want the minimum product xy

Answer 21

The minimum val of the product xy

Answer 22

i never encountered a problem like that in calc, i think you may have interpreted the question wrong

Answer 23

:/

Answer 24

The question is the beginning of the thread

Answer 25

yea it asks for the product y, it doesn't say multiply x and y together

Answer 26

I meant xy

Answer 27

Sorry, that was a typo

Answer 28

that doesn't make sense for this question, i took AB calc last year and never encountered a problem like this so I don't know how to help, sorry

Answer 29

Its ok. Thanks anyways

Answer 30

"If y=2x^2-8x, what is the minimum value of the product xy?"

P = xy = x (2x^2-8x) = ?? and then differeniate.

easier?