Exercise 12 — Active Calculus Multivariable

The Heat Index, $I$ , (measured in apparent degrees F) is a function of the actual temperature $T$ outside (in degrees F) and the relative humidity $H$ (measured as a percentage). A portion of the table which gives values for this function, $I(T,H)$ , is reproduced in Table.

Heat index.
T $\downarrow \backslash$ H $\rightarrow$	70	75	80	85
90	106	109	112	115
92	112	115	119	123
94	118	122	127	132
96	125	130	135	141

State the limit definition of the value $I_{TT}(94,75)$ . Then, estimate $I_{TT}(94,75)$ , and write one complete sentence that carefully explains the meaning of this value, including units.
State the limit definition of the value $I_{HH}(94,75)$ . Then, estimate $I_{HH}(94,75)$ , and write one complete sentence that carefully explains the meaning of this value, including units.
Finally, do likewise to estimate $I_{HT}(94,75)$ , and write a sentence to explain the meaning of the value you found.

Long, Keller & Schlicker, Active Calculus Multivariable, §11.5 Second-Order Partial Derivatives, Exercise 12

AI Tutor