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Answer :
To determine whether the statement [tex]\( f'(t) < 0 \)[/tex] is true or false, let's analyze the situation:
1. Understanding the context:
- We have a function [tex]\( T = f(t) \)[/tex] that represents the temperature of a cold yam placed in a hot oven as time [tex]\( t \)[/tex] increases.
- The derivative [tex]\( f'(t) \)[/tex] represents the rate of change of the temperature with respect to time.
2. Interpreting [tex]\( f'(t) < 0 \)[/tex]:
- If [tex]\( f'(t) < 0 \)[/tex], it indicates that the function [tex]\( f(t) \)[/tex] is decreasing over time. In simpler terms, the temperature of the yam would be going down as time goes on.
3. Analyzing the situation:
- A cold yam is placed in a hot oven. We expect the yam to heat up because the oven is hotter than the yam.
- Therefore, the temperature of the yam should increase over time, meaning the function [tex]\( f(t) \)[/tex] should increase as [tex]\( t \)[/tex] increases.
4. Conclusion:
- For the temperature of the yam to increase, [tex]\( f'(t) \)[/tex] must be greater than 0. This means the temperature is rising, not falling.
- Hence, the statement [tex]\( f'(t) < 0 \)[/tex] is not correct in this context.
Therefore, the statement is False.
1. Understanding the context:
- We have a function [tex]\( T = f(t) \)[/tex] that represents the temperature of a cold yam placed in a hot oven as time [tex]\( t \)[/tex] increases.
- The derivative [tex]\( f'(t) \)[/tex] represents the rate of change of the temperature with respect to time.
2. Interpreting [tex]\( f'(t) < 0 \)[/tex]:
- If [tex]\( f'(t) < 0 \)[/tex], it indicates that the function [tex]\( f(t) \)[/tex] is decreasing over time. In simpler terms, the temperature of the yam would be going down as time goes on.
3. Analyzing the situation:
- A cold yam is placed in a hot oven. We expect the yam to heat up because the oven is hotter than the yam.
- Therefore, the temperature of the yam should increase over time, meaning the function [tex]\( f(t) \)[/tex] should increase as [tex]\( t \)[/tex] increases.
4. Conclusion:
- For the temperature of the yam to increase, [tex]\( f'(t) \)[/tex] must be greater than 0. This means the temperature is rising, not falling.
- Hence, the statement [tex]\( f'(t) < 0 \)[/tex] is not correct in this context.
Therefore, the statement is False.
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