# Thread: Show that there is only one value of x for which P is stationary..?

1. ## Show that there is only one value of x for which P is stationary..?

Sorry if I posted this in the wrong place.

Two numbers x and y are such that 2x + y = 12.
The product P is formed by multiplying the first number by the square of the second number so that P = xy²

P = 4x³ - 48x² + 144x

I worked out the two values of x for which dP/dx = 0
They are x = 6 and x = 2 (hopefully!)

Now it says : The values of x and y must both be positive, show that there is only one value of x for which P is stationary.

How do I do this?

2. Originally Posted by Jayde
Sorry if I posted this in the wrong place.

Two numbers x and y are such that 2x + y = 12.
The product P is formed by multiplying the first number by the square of the second number so that P = xy²

P = 4x³ - 48x² + 144x

I worked out the two values of x for which dP/dx = 0
They are x = 6 and x = 2 (hopefully!)

Now it says : The values of x and y must both be positive, show that there is only one value of x for which P is stationary.

How do I do this?