Question

The table below shows the temperature (in °F) t hours after midnight in Phoenix on March 15. The table shows values of this function recorded every two hours.

Estimate the value of T′(10). Give units in your answer.
What is the meaning of T′(10)?

Answer 1

t 0 2 4 6 8 10 12 14
T 73 73 70 68 73 80 86 89

Answer 2

@jdoe0001 @iambatman @dan815 @Data_LG2 @e.mccormick @jim_thompson5910

Answer 3

\[\Large T'(10) \approx \frac{T(12)-T(8)}{12-8} = ??\]

notice how I'm looking to the nearest neighbor of t = 10 (t = 12 and t = 8) to set up a secant slope. The secant slope is the best approximation to the tangent in this case.

Answer 4

okay so 13/8 or 3.25

Answer 5

what r the units? @jim_thompson5910

Answer 6

@Data_LG2

Answer 7

\[\Large T'(10) \approx \frac{T(12)-T(8)}{12-8}\]

\[\Large T'(10) \approx \frac{86-73}{12-8}\]

\[\Large T'(10) \approx \frac{13}{4}\]

\[\Large T'(10) \approx 3.25\]

Answer 8

I think you meant to say 13/4 instead of 13/8

Answer 9

the units are "degrees per hour"

Answer 10

since we have "degrees" in the numerator
and "hour" in the denominator

so it's basically the instantaneous change in temp per hour (the approximate value)

Answer 11

What is the meaning of T′(10)?

It's basically asking "what is the instantaneous change in temp per hour at t = 10?" and the answer is approximately "3.25 degrees per hour".

Answer 12

@jim_thompson5910 thanks :)