- #1
Khronos
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Hi everyone, I need a little bit of help with an optimization problem and finding the critical numbers. The question is a follows:
Question:
Between 0°C and 30°C, the volume V ( in cubic centimeters) of 1 kg of water at a temperature T is given approximately by the formula:
V = 999.87 − 0.06426T + 0.0085043T2 − 0.0000679T3
Find the temperature at which water has its maximum density. (Round your answer to four decimal places.)
I have done the following steps:
Re-write equation into scientific notation:
V(t)=-6.79x10-5T3+8.5043x10-3T2-6.426x10-2T+999.87
Found Derivative using Power Rule:
V'(t)=-2.037x10-4T2+1.70086x10-2T-6.426x10-2
I need to find critical points, where V'(t)=0 or V'(t)=und.
There are no obvious factors and I need help to find the zero's of the derivative.
Any help would be greatly appreciated.
Question:
Between 0°C and 30°C, the volume V ( in cubic centimeters) of 1 kg of water at a temperature T is given approximately by the formula:
V = 999.87 − 0.06426T + 0.0085043T2 − 0.0000679T3
Find the temperature at which water has its maximum density. (Round your answer to four decimal places.)
The Attempt at a Solution
I have done the following steps:
Re-write equation into scientific notation:
V(t)=-6.79x10-5T3+8.5043x10-3T2-6.426x10-2T+999.87
Found Derivative using Power Rule:
V'(t)=-2.037x10-4T2+1.70086x10-2T-6.426x10-2
I need to find critical points, where V'(t)=0 or V'(t)=und.
There are no obvious factors and I need help to find the zero's of the derivative.
Any help would be greatly appreciated.