Problem 5.15 The temperature in a certain region of space is given by T = To - A(2x² + y? + 2?) (in kelvin). Distances are in meters and the constant 4 has the value 0.5 kelvin/m². The value of To is 300 K. (a) At point (1,2,2) what is the direction and rate (in K/m) of marimum temperature increase? (b) If you move one meter in that direction what is the temperature at the new position? (c) The temperature at the new position as calculated by the formula is not equal to the value odtained by multiplying the rate of temperature decrease by the displacement. Explain this discrepancy.

Problem 5.15 The temperature in a certain region of space is given by T = To - A(2x² + y? + 2?) (in kelvin). Distances are in meters and the constant 4 has the value 0.5 kelvin/m². The value of To is 300 K. (a) At point (1,2,2) what is the direction and rate (in K/m) of marimum temperature increase? (b) If you move one meter in that direction what is the temperature at the new position? (c) The temperature at the new position as calculated by the formula is not equal to the value odtained by multiplying the rate of temperature decrease by the displacement. Explain this discrepancy.