An individuals utility depends upon the consumption of goods x and y,

I have to find the utility maximisation of x and y,

(1)

(2)

Multiply (1) by 2 = (3)

(4)

(3)-(4), after rearranging and substitution,

x = 8, y = 8

To check these are the maximum points,

Find cross partial derivitives,

= 16 > 0

3 conditions meet = maximum

I then have to use the total differential of the function to find an expression for the slope of any curve.

Slope of curve =

This is where i become a little stuck as to what I should do next.