3. [5 marks] Suppose, at T = 0C, a sample of water has volume Vo = 1000 cm3. If the temperature of the water is increased then the volume of the water will change and can be approximated by: V(T) = 1000 - 1 250000 (1773 -212572 + 16184T) , 0 ST S 10. (a) Determine the temperature of the water when it's at its lowest volume given that this occurs when V'(T) = 0. Include units in your final result. (b) Using the result in part (a), find the lowest water volume for T E [0, 10]. Result may be round to 2 decimal places. Include units in your final result. [Note: The small decrease in water volume is esssential to a number of ecosystems. Consider a lake where the top of the water is being warmed to about 4C. The warmer water becomes denser and, therefore, sinks to the bottom. If the temperature suddenly decreases, freezing the lake over, the warm water is trapped below allowing fish to survive the winter.]