NIMCET 2017 Question Paper with solutions

For critical points

δf

δx

= 0 and

δf

δy

= 0
∴ 2x -2 = 0 and 4y + 4 = 0
⇒ x = land y = -1
Hence, critical point of the given function is (1, -1).
The given function is maximum at (1, -1), if
rt - s2 > 0 and r < 0
And minimum at (1, -1), if rt - s2 > 0 and r > 0
For maximum and minimum
r =

δ2f

δx2

= 2 ,
t =

δ2f

δy2

= 4
and s =

δ2f

δxδy

= 0
Clearly, by putting the value of r, t and a, we get r > 0 and rt - s2 > 0
Hence, the given function is minimum at (1, - 1).