Let f(t) be the temperature at time t where you live and suppose that at time t

Question

Let f(t) be the temperature at time t where you live and suppose that at time t = 2 you feel uncomfortably hot. What happens to the temperature in each case? (a) f '(2) = ?2, f ''(2) = 6 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 '(2) = 2, f ''(2) = ?6 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). (c) f '(2) = 2, f ''(2) = 6 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 '(2) = ?2, f ''(2) = ?6 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).

Explanation / Answer

Let f(t) be the temperature at time t where you live andsuppose that at time t=3 you feel uncomfortably hot. How do youfeel about the given data in each case? (a) f '(3)= 2, f "(3)= 4 (b) f '(3)= 2, f "(3)= -4 (c) f '(3)= -2, f "(3)= 4 (d) f '(3)= -2, f "(3)= -4 Since you feel uncomfortably hot at time t = 3 then thefunction is increasing. (a) f '(3) = 2 and f ''(3) = 4 Makes sensesince the function is increasing (b) f '(3) = 2 and f ''(3) = -4 doesn't make sense since thefunction is increasing its impossible it goes from 2 to -4 (c) f '(3) = -2 and f ''(3) = 4 Well f '(3) = -2 is notuncomfortably hot (we know f (t) feels uncomfortably hot) so thisis impossible as well. (d) f '(3) = -2 and f ''(3) = -4 doesn't make sense becausef(t) is uncomfortably hot, and the 1st derivative and secondderivative seems uncomfortably cold o_O. Thus, f '(3) = 2 and f ''(3) = 4 is increasing the answer isa

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