Chapter 1, Problem 83IAE

The following equation can be used to relate the density of Equid water to Celsius temperature in the range from 0 °C to about 20 °C:

   $d\left(g/c{m}^3\right)=\frac{0.99984+\left(1.6945\times {10}^{-2}t\right)-\left(7.987\times {10}^{-6}{t}^2\right)}{1+\left(1.6880+{10}^{-2}t\right)}$
a. To four significant figures, determine the density of water at 10 °C.
b. At what temperature does water have a density of 0.99860 g/cm³?
c. In the following ways, show that the density passes through a maximum somewhere in the temperature range to which the equation applies.
i. by estimation
ii. by a graphical method
iii. by a method based on differential calculus