# Math Help - Why is my upper bound answer wrong?

1. ## Why is my upper bound answer wrong?

A freshly poured cup of coffee is left in a room which is maintained at a constant temperature, lower than the initial temperature of the coffee. In this situation, the graph of the temperature of the coffee against time will be decreasing and concave up.
At , the temperature of the coffee is , and is decreasing at a rate of /min. At (minutes), the temperature of the coffee is .

a) Make a rough sketch of the vs graph of the coffee which displays the information given so far.

b) Using this information, provide upper and lower estimates of the temperature of the coffee at minutes:

My work is attached as a pdf file.

2. Originally Posted by s3a
A freshly poured cup of coffee is left in a room which is maintained at a constant temperature, lower than the initial temperature of the coffee. In this situation, the graph of the temperature of the coffee against time will be decreasing and concave up.
At , the temperature of the coffee is , and is decreasing at a rate of /min. At (minutes), the temperature of the coffee is .

a) Make a rough sketch of the vs graph of the coffee which displays the information given so far.

b) Using this information, provide upper and lower estimates of the temperature of the coffee at minutes:

My work is attached as a pdf file.
(0,100) (30,44) ... $\frac{\Delta T}{\Delta t} = \frac{44-100}{30-0}$

$T_u = 100 -\frac{56}{30}(20) = 62.667$

3. That was such a stupid mistake. Thanks!