Q1) The temperature T(x; y) in the X-Y plane at the point (x; y) is given by
T(x; y) = 4x^2 - y^2 + 2y:
Find the unit vector giving the direction an ant at position (-1; 4) should move
in order to cool off as quickly as possible.

2. Suppose the ant in Q.1 is restricted to move on the circle of radius 1 centred at
(0; 0). Use the method of Lagrange multipliers to Find the points(s) on this circle
of minimum and maximum temperature.

Hi, I've solved Q1. Please help with Q2..

Question

Q1) The temperature T(x; y) in the X-Y plane at the point (x; y) is given by
T(x; y) = 4x^2 - y^2 + 2y:
Find the unit vector giving the direction an ant at position (-1; 4) should move
in order to cool off as quickly as possible.

2. Suppose the ant in Q.1 is restricted to move on the circle of radius 1 centred at
(0; 0). Use the method of Lagrange multipliers to Find the points(s) on this circle
of minimum and maximum temperature.

Hi, I've solved Q1. Please help with Q2..