There is a bug crawling on a metal plate. The temperature at a point (x, y) on this metal plate isT(x, y), measured in degrees Celsius.
A bug crawls so that its position after t seconds is given by:
x = 2 + (1/4)t, y = √(1+t),
where x and y are measured in centimeters.
The temperature function satisfies Tₓ (4,3) =-5 and Tᵧ(4,3) = 5.
(You should assume that the temperature at a point on this metal plate does not change over time.)
(a) Let's say that there is also a spider that is stationary and located at (7,6) on the metal plate. Therefore the position at time t for the spider is At the spider's position after t = 8 seconds how fast is the temperature that the spider feels changing per second?
(b) At the bug's position after t = 8 seconds, how fast is the temperature that the bug feels changing per second? (i. e. What is ∂T/∂t for the bug?)
(c) At the bug's position after t = 8 seconds, how fast is the temperature that the bug feels changing per centimeter? (i. e. What is the change in temperature in the direction the bug is moving at t = 8?)