Minimization and Differentiation: Find temp w/ max volume

[sofiaahmed]

Hi. This is my problem:

Between 0° and 30° Celsius, the volume V (in cubic centimeters) of 1 kg of water at a temperature T is given approximately be the formula:

. . .V = 999.87 - 0.06426T + 0.0085043T^2 - 0.0000679T^3

Find the temperature at which water has its maximum density.

I took the derivative and then used the quadratic formula to come up with: T=79.550 and T=3.948

Are these values correct? Doesn't the answer have to be between 0-30 degrees? Please help me.

 

[galactus]

3.9 is between 0 and 30, isn't it?.

 

[sofiaahmed]

Is there a way I can check to make sure this is the right answer?