Answer :
Sure! Let's tackle this problem step-by-step:
### A. What is the sign of [tex]\( f^{\prime}(t) \)[/tex]?
The derivative [tex]\( f^{\prime}(t) \)[/tex] represents the rate of change of the turkey's temperature over time. Since the turkey is being placed in a hot oven, the temperature of the turkey is increasing as time passes. Therefore, the rate of change of temperature, [tex]\( f^{\prime}(t) \)[/tex], is positive, indicating a rising temperature.
### B. What are the units of [tex]\( f^{\prime}(35) \)[/tex]?
The derivative [tex]\( f^{\prime}(t) \)[/tex] describes the rate of change of temperature with respect to time. Since the function [tex]\( f(t) \)[/tex] outputs temperature in degrees Fahrenheit and the input [tex]\( t \)[/tex] is in minutes, the units of [tex]\( f^{\prime}(t) \)[/tex] would be the change in temperature per unit of time. Therefore, the units of [tex]\( f^{\prime}(35) \)[/tex] are degrees Fahrenheit per minute.
### C. Explain the meaning of the statement [tex]\( f(35) = 106 \)[/tex] in the context of the problem.
The function [tex]\( f(t) \)[/tex] represents the temperature of the turkey at a given time [tex]\( t \)[/tex]. So, the statement [tex]\( f(35) = 106 \)[/tex] means that after 35 minutes in the oven, the turkey's temperature is 106 degrees Fahrenheit.
### D. What is the meaning of the statement [tex]\( f^{\prime}(35) = 3 \)[/tex]?
The statement [tex]\( f^{\prime}(35) = 3 \)[/tex] indicates that at 35 minutes, the turkey's temperature is increasing at a rate of 3 degrees Fahrenheit per minute. This tells us how quickly the temperature is rising at that specific moment in time.
I hope this breakdown helps you understand the problem better! If you have any more questions, feel free to ask.
### A. What is the sign of [tex]\( f^{\prime}(t) \)[/tex]?
The derivative [tex]\( f^{\prime}(t) \)[/tex] represents the rate of change of the turkey's temperature over time. Since the turkey is being placed in a hot oven, the temperature of the turkey is increasing as time passes. Therefore, the rate of change of temperature, [tex]\( f^{\prime}(t) \)[/tex], is positive, indicating a rising temperature.
### B. What are the units of [tex]\( f^{\prime}(35) \)[/tex]?
The derivative [tex]\( f^{\prime}(t) \)[/tex] describes the rate of change of temperature with respect to time. Since the function [tex]\( f(t) \)[/tex] outputs temperature in degrees Fahrenheit and the input [tex]\( t \)[/tex] is in minutes, the units of [tex]\( f^{\prime}(t) \)[/tex] would be the change in temperature per unit of time. Therefore, the units of [tex]\( f^{\prime}(35) \)[/tex] are degrees Fahrenheit per minute.
### C. Explain the meaning of the statement [tex]\( f(35) = 106 \)[/tex] in the context of the problem.
The function [tex]\( f(t) \)[/tex] represents the temperature of the turkey at a given time [tex]\( t \)[/tex]. So, the statement [tex]\( f(35) = 106 \)[/tex] means that after 35 minutes in the oven, the turkey's temperature is 106 degrees Fahrenheit.
### D. What is the meaning of the statement [tex]\( f^{\prime}(35) = 3 \)[/tex]?
The statement [tex]\( f^{\prime}(35) = 3 \)[/tex] indicates that at 35 minutes, the turkey's temperature is increasing at a rate of 3 degrees Fahrenheit per minute. This tells us how quickly the temperature is rising at that specific moment in time.
I hope this breakdown helps you understand the problem better! If you have any more questions, feel free to ask.
