You put a yam in a hot oven, maintained at a constant temperature of 200^◦C. As the yam picks up heat from the oven, its temperature rises.
(a) Draw a possible graph of the temperature T of the yam against time t (minutes) since it is put into the oven. Explain any interesting features of the graph, and in particular explain its concavity.
(b) At t = 30, the temperature T of the yam is 120^◦ and increasing at the (instantaneous) rate of 2^◦/min. Using this information and the shape of the graph, estimate the temperature at time t = 40.
(c) In addition, you are told that at t = 60, the temperature of the yam is 165^◦. Can you improve your estimate of the temperature at t = 40?
(d) Assuming all the data given so far, estimate the time at which the temperature of the yam is 150^◦.