1.Between 0°C and 30°C, the volume V ( in cubic centimeters) of 1 kg of water at a temperature T is given approximately by the formula
V = 999.87 − 0.06426T + 0.0085043T2 − 0.0000679T3
Find the temperature at which water has its maximum density. (Round your answer to four decimal places.)
2.If a and b are positive numbers, find the maximum value of f(x) = xa(8−x)b on the interval
0 ≤ x ≤ 8.
3.Sketch the graph of f by hand and use your sketch to find the absolute and local maximum and minimum values of f. (Use the graphs and transformations of Sections 1.2 and 1.3. Enter your answers as a comma-separated list. If an answer does not exist, enter DNE.)