Suppose a gram of ice is at a temperature of -100°C. The graph shows the temperature of the ice as increasing numbers of calories of heat are applied. It takes 80 calories to melt one gram of ice at 0°C into water, and 540 calories to boil one gram of water at 100°C into steam.

(a) Where is this graph discontinuous?
(b) Where is this graph not differentiable?
(c) Sketch the graph of the derivative.

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200 -100 T (degrees C) 50 500 Q (calories)