 # Y 3x 7

## Y 3x 7

### What is the minimum uct of y = 3x7, x> 0, x

Let's say P = x²y, then

P = x²y

.. = x² (3x7)

.. = 3xÃÂ³ 7x7

Take the first derivative

P = 9x² 14x

.. = x (9 x 14)

.. = 0 to x = 0 and x = 14/9

Since x must be greater than z,

We can only consider x = 14/9.

Now the question is:

What is the minimum x = 14/9 of P?

Consider another derivative of P.

P = 18 x 14

For x = 14/9, P = 18 (14/9) 14 = 14, which is positive.

P> 0 to x = 14/9.

So P x = 14/9 is concave and therefore

P is the minimum with respect to x = 14/9.

Now for x = 14/9

y = 3x7

y = 3 (14/9) 7

y = 7/3

So x² is at least y.

P = x²y

P = (14/9) ² (7/3)

p = 5.646

____________

5,646

____________

If y = 3x7, x> 0, what is the minimum uct of x²y?

____________

Let's say P = x²y, then

P = x²y

.. = x² (3x7)

.. = 3xÃÂ³ 7x7

Take the first derivative

P = 9x² 14x

.. = x (9 x 14)

.. = 0 to x = 0 and x = 14/9

Since x must be greater than z,

We can only consider x = 14/9.

_____________

Now the question is:

What is the minimum x = 14/9 of P?

Consider another derivative of P.

P = 18 x 14

For x = 14/9, P = 18 (14/9) 14 = 14, which is positive.

P> 0 to x = 14/9.

So P x = 14/9 is concave and therefore

P is the minimum with respect to x = 14/9.

_______________

Now for x = 14/9

y = 3x7

y = 3 (14/9) 7

y = 7/3

_______________

So x² is at least y.

P = x²y

P = (14/9) ² (7/3)

p = 5.646

______________________________