Chain rule - calc

Question

The table below gives the height of a rocket as a function time,h(t).

Units are in the table.

h (m)	0	66	164	295	457	651	878	1138	1429	1753	2108
t (s)	0	1	2	3	4	5	6	7	8	9	10

Air temperature is a function of height: T(h) = 300 − h/200

with T in kelvins and h as above. There is a temperature sensor on the rocket. How fast is the temperature, as measured by this sensor, changing at the instant when t = 6 seconds?

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Answer 1

T(h) = 300 -h/200

T'(h) = -1/200 = -0.005 degrees per second

T'(6) = -1/200 = -0.005 degrees per second

the rate of change is the same at any value of h

but the table of values is very different from the function T(h) = 300- h/200

T(878) = 300 -878/200 = 300-4.39 = 295.61 not 6

the function T(h) is a linear function, a straight line

the table of values is not a linear relationship.