3. The temperature T in °C at (x, y) in centimeters is T (x, y) = 100 - x$^2$ - y$^2$. Use the
gradient in your calculations.
a. In which direction should a heat-seeking bug move from the point (3, -1) to
increase its temperature fastest?
b. For part a, what is the maximum rate of change of temperature with respect to
distance?
c. Find the rate of change in the direction of \(\vec{v} = <1, 2>\).
d. Find the linear approximation of f(3, 9).