1. ## What to do?

Hi
i got this question and not sure what its about:

Find the value of x that minimises
y = 8X^2 (400/X)
for positive x.

Give the required x both exactly (i.e. as a surd).

What do i do?
This is what i started doing but no idea what else:
=> y=8x^2+(400/x)
=> 16x-400x^(-2)
==> 16x-400x^(-2) = 0

Thanks

2. Originally Posted by taurus
Hi
i got this question and not sure what its about:

Find the value of x that minimises
y = 8X^2 (400/X) Mr F says: So there's meant to be a + between these two terms?

for positive x.

Give the required x both exactly (i.e. as a surd).

What do i do?
This is what i started doing but no idea what else:
=> y=8x^2+(400/x)
=> 16x-400x^(-2)
==> 16x-400x^(-2) = 0

Thanks
So solve the equation by multiplying through by x^2 to end up with x^3 = 25 => x = (25)^(1/3)....... Now use the sign test to check the nature of the solution.

3. kind of confused still

and yes theres meant to be a plus

4. Originally Posted by taurus
kind of confused still

and yes theres meant to be a plus
Did you multiply 16x-400x^(-2) = 0 through by x^2?? Show me what you get.

5. ok so gives:

16x^2 + 400x^(-4)

6. Originally Posted by taurus
ok so gives:

16x^2 + 400x^(-4)
Wrong for several reasons, including the fact that there's no = sign and therefore you have not given an equation.

16x-400x^(-2) = 0 multiplied through by x^2 gives 16x^3 - 400 = 0.

Do you understand that x^(-2) times x^2 = x^0 = 1? You need to revise your basic algebraic skills.

7. oh ya sorry, i was not thinking correctly

what do i do after that?

8. Originally Posted by taurus
oh ya sorry, i was not thinking correctly

what do i do after that?
I can't see Mr. Fantastic beeing around so I'll take over:

Separate variable and constant:

$16x^3-400=0~\implies~16x^3=400~\implies~x^3=25 ~\implies~x=\sqrt[3]{25} \approx 2.924...$