(Mean Value Theorem) When an object is removed from a furnace and placed in an environment with a constant temperature of 90*F, its core temperature is 1500*F. Five hours later the core temperature is 390*F. Explain why there must exist a time in the interval when the temperature is decreasing at a rate of 222*F per hour.
-Thank you.

Question

(Mean Value Theorem) When an object is removed from a furnace and placed in an environment with a constant temperature of 90*F, its core temperature is 1500*F. Five hours later the core temperature is 390*F. Explain why there must exist a time in the interval when the temperature is decreasing at a rate of 222*F per hour.
-Thank you.

dumbcow · Answer

the answer comes directly from the mean value thm

$$f'(c) = \frac{f(b) -f(a)}{b-a}$$
$$f'(c) = \frac{1500 -390}{5-0} = 220$$

anonymous · Answer

@dumbcow i thought f(b)=390 (the final point), so i got f'(c)= (390-1500)/5 is -555.
It's decreasing so the slope must be negative??

anonymous · Answer

i mean -222, not -555

dumbcow · Answer

yes you are correct, sorry i wasnt paying attention to the details