Find the upper and lower estimates for the temperature? The given values are attached as a picture! Thanks.
(note: the stone's temperature is between these 2 temperature but can't actually be either of them)
the graphs below might help the explanation make more sense.
the highest temperature of the stone after 4 minutes is if the stone continues increasing at 15°C/min (the initial rate) (see first graph). since the temperature graph is concave down, the maximum temperature of the stone after 4 minutes will be an infinitely small amount less than this linear approximation:
when x = 4, y = 15(4)+13 = 73, the maximum.
the lowest temperature of the stone after 4 minutes is if the stone temperature increases at a rate just enough to reach 79°C by 5 mins (see second graph). to find the linear approximation, first find the slope of the line containing (0,13) and (5,79)
slope = 66/5
when x = 4, y = 66/5(4)+13 = 65.8, the minimum