Answer:
The answer to your question is: T = 4°C
Explanation:
Data
Temperature 0°C to 30°C
mass = 1 kg
V = 999.87 − 0.06426T + 0.0085043T² − 0.0000679T³
T = ? of maximum density
Density = mass / volume, If we look for the maximum density, the volume must be a minimum.
Then, we need to calculate the first and second derivative to find the minimum.
dV/dT = − 0.06426 + 0.017T − 0.000204T²
Solve the quadratic equation, solutions
T1 = 3.97 T2 = 79.36
Second derivative
dV/dT = 0.017 - 0.000408T
Evaluate T1 and T2 in the second derivative to find their sign, if it is positive, there is a minimum and if the sign is negative, it is a maximum.
dV/dT = 0.017 - 0.000408(3.97) = 0.015 positive
dV/dT = 0.017 - 0.000408(79.36) = -0.015 negative
Then
T1 = 3.97 ≈ 4°C is a minimum
T2 = 79.364 is a maximum
Finally, in T1 there is a minimum, and the density will be the highest, becuase the volume will be minimum.