The temperature at a point ( x , y ) is T ( x , y ), measured in degrees Celsius. A bug crawls so that its position after t seconds is given by x = 1 + t , y = 2 + 1 3 t , where x and y are measured in centimeters. The temperature function satisfies T x ( 2 , 3 ) = 4 and T y ( 2 , 3 ) = 3 . How fast is the temperature rising on the bug’s path after 3 seconds?
The temperature at a point ( x , y ) is T ( x , y ), measured in degrees Celsius. A bug crawls so that its position after t seconds is given by x = 1 + t , y = 2 + 1 3 t , where x and y are measured in centimeters. The temperature function satisfies T x ( 2 , 3 ) = 4 and T y ( 2 , 3 ) = 3 . How fast is the temperature rising on the bug’s path after 3 seconds?
Solution Summary: The author explains how to find the temperature rise on the bug's path by using the chain rule.
The temperature at a point (x, y) is T(x, y), measured in degrees Celsius. A bug crawls so that its position after t seconds is given by
x
=
1
+
t
,
y
=
2
+
1
3
t
, where x and y are measured in centimeters. The temperature function satisfies
T
x
(
2
,
3
)
=
4
and
T
y
(
2
,
3
)
=
3
. How fast is the temperature rising on the bug’s path after 3 seconds?
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