M Let f(t) be the temperature at time t where you live and suppose that at time t = 1 you feel uncomfortably hot. What happens to the temperature in each case? (a) f'(1) = 2, f "(1) = 2 The temperature is increasing, and the rate of increase is increasing. The temperature is increasing, but the rate of increase is decreasing. The temperature is decreasing, but the rate of change is increasing (becoming less negative). The temperature is decreasing, and the rate of change is decreasing (becoming more negative). (b) f'(1) = 2, f "(1) = -2 (c) The temperature is increasing, and the rate of increase is increasing. The temperature is increasing, but the rate of increase is decreasing. The temperature is decreasing, but the rate of change is increasing (becoming less negative). The temperature is decreasing, and the rate of change is decreasing (becoming more negative). f'(1)-2, "(1) = 2 The temperature is increasing, and the rate of increase is increasing. The temperature is increasing, but the rate of increase is decreasing. The temperature is decreasing, but the rate of change is increasing (becoming less negative). The temperature is decreasing, and the rate of change is decreasing (becoming more negative). (d) f'(1)=-2, f "(1) = -2 The temperature is increasing, and the rate of increase is increasing. The temperature is increasing, but the rate of increase is decreasing. The temperature is decreasing, but the rate of change is increasing (becoming less negative). The temperature is decreasing, and the rate of change is decreasing (becoming more negative).