We wish to minimise z=4x2+3y2 which can be rewritten as z=4(8+y)2+3y2.
Min value can be found by completing the square.
Could you not differentiate z=4x2+3y2, set equal to 0, substitute x=8+y, find the value of y, find the value of x, and resubstitute back into your equation for z?
Could you not differentiate z=4x2+3y2, set equal to 0, substitute x=8+y, find the value of y, find the value of x, and resubstitute back into your equation for z?
Yes this is a valid approach, but this thread was originally in GCSE forum so I didn’t suggest this approach for that level.