A model for the specific gravity of water S is

where T is the water temperature in degrees Celsius.

(a) Use the second derivative to determine the concavity of S.

(b) Use a computer algebra system to find the coordinates of the maximum value of the function.

(c) Use a graphing utility to graph the function over the specified domain. (Use a setting in which 0.996 ≤ S ≤ 1.001.)

(d) Estimate the specific gravity of water when T = 20°.

S= 5.755 108 -T3. 8.521 106 -T + 6.540 10 T+0.99987, 0 < T < 25