A graphing calculator is required for these problems.
1. The temperature of water in a tub at time t is modeled by a strictly increasing, twice-differentiable function W, where Wt is measured in degrees Fahrenheit and t is measured in minutes. At time t 0, the temperature of
the water is 55F. The water is heated for 30 minutes, beginning at time t 0. Values of Wt at selected times t for the first 20 minutes are given in the table above.
(a) Use the data in the table to estimate $\large W'(12)$. Show the computations that lead to your answer.

Question

A graphing calculator is required for these problems.
1. The temperature of water in a tub at time t is modeled by a strictly increasing, twice-differentiable function W, where Wt is measured in degrees Fahrenheit and t is measured in minutes. At time t  0, the temperature of
the water is 55F. The water is heated for 30 minutes, beginning at time t  0. Values of Wt at selected times t for the first 20 minutes are given in the table above.
(a) Use the data in the table to estimate $\large W'(12)$. Show the computations that lead to your answer.

preetha · Answer

Wait, let me post the table.

preetha · Answer

t (minutes)
0    4     9    15    20
Wt (degrees Fahrenheit)
55.0 57.1 61.8  67.9 71.0

dbzfan836 · Answer

@Broskishelleh may be able to help, or @satellite73 would be better for assistance

dbzfan836 · Answer

@Preetha

aum · Answer

You can use a regression calculator to fit a quadratic function (least square fit) and then find w(12).

anonymous · Answer

looks kind of linear we can make an equation would help if we know if it was polynomial or exponential http://www.wolframalpha.com/input/?i=%280%2C55%29%2C%284%2C57.1%29%2C%289%2C61.8%29%2C%2815%2C67.9%29%2C%2820%2C71%29

dbzfan836 · Answer

Alright, anybody here that does not know the answer, please leave to help others. it is unfair for alot of people to be at a question that needs an answer/explanation

anonymous · Answer

here is the polynomial i would ignore the first term http://www.wolframalpha.com/input/?i=polynomial+%280%2C55%29%2C%284%2C57.1%29%2C%289%2C61.8%29%2C%2815%2C67.9%29%2C%2820%2C71%29

broskishelleh · Answer

I know now what to do:
w(12) = w(15) - w(9)/ 15 - 9 = 67.9 - 61.8/ 6

anonymous · Answer

says to use a graphing calculator, so i imagine wolfram is the way to go

xapproachesinfinity · Answer

how many medals will i get if i answered lol

broskishelleh · Answer

This would make the answer 1.017 degrees Fahrenheit increasing a minute approximately

aum · Answer

Given 5 points, a fourth degree polynomial will be an EXACT fit for the given data.

anonymous · Answer

@Broskishelleh  with that method you would make the answer 
$$61.8+1.017$$

broskishelleh · Answer

Ah, correct I am sorry for my forgetfullness

broskishelleh · Answer

Was I correct @satellite73

anonymous · Answer

sure why not?  it says estimate, and it says the function is increasing so split the difference

broskishelleh · Answer

I can't believe I am right, I just answered the owners question...WHAT A GREAT HONOR!

broskishelleh · Answer

@Preetha Was it a good answer?

camerondoherty · Answer

Preetha is Just looking around
Aka: Offline
Lol
But good Job c:

preetha · Answer

Naah.  I am here.  Thanks for that awesome discussion.  Hope to see many more of these discussions this year!

zarkon · Answer

this data is highly correlated to a quadratic function.  Do a quadratic regression and find the derivative of the best fit quadratic evaluated at 12

broskishelleh · Answer

@Preetha Can I message you? I have some questions...

anonymous · Answer

Im sure she will

preetha · Answer

Yes, you can certainly message me!

preetha · Answer

Thanks everyone again.