Let T(x,y) denote the temperature at location (x,y). You are given the following information.

• The rate of change of T at the point A(1,2) in the direction ~ w = ˆ i + ˆ j is √8.

• The rate of change of T at the point A(1,2) in the direction ~ v = 4ˆ i −3ˆ j is 6. • The temperature at A(1,2) is 20.

(a) From the point A(1,2), in which direction would you head to cool off most rapidly?

(b) What is the minimum rate of change of temperature at point A(1,2)?

(c) Estimate the temperature at the point (0.97,2.02) to two decimal places.