Find all relative extrema of the function. Use the Second Derivative Test where applicable. (If an answer does not exist, enter DNE.) f(x) = x6\" 6 relative maximum (X, y) = ( DNE ) relative minimum (x, y) = ( ) X The graph shows the temperature T, in degrees Fahrenheit, of molten glass t seconds after it is removed from a kiln. (0.1500) 79 (a) Find lim T- r>0+ :x o. What does this limit represent? O This is the natural temperature of glass. 0 This is the initial rate at which the glass is cooling. This is the temperature of the kiln. O This is the temperature of the room. (b) Find lim T- [am :2: .. What does this limit represent? O This is the natural temperature of glass. 0 This is the initial rate at which the glass is cooling. 0 This is the temperature of the kiln. This is the temperature of the room. Find two positive numbers whose sum is 210 and whose product is a maximum. (a) Analytically complete six rows of a table such as the one below. (The first two rows are shown.) First Second Number, x Number Product, p 210 60 60(210 60) = 9 000 : 210 7O 70(210 70) = 9 800 210 80 80(210 80): :l x 210 90 90(210 90) = :l x 210 100 100(210 100): |:] g - 210 11o 110(210 110): |:l g (b) Write the product P as a function of x. P(x) = 3f (c) Use calculus to find the critical number of the function in part (b). Then find the two numbers. (Enter your answers as a comma-separated list.)