A hot dish is placed in a refrigerator and then removed from the refrigerator after eighty-five minutes. Suppose that the function D(t) represents the temperature of the dish, in degrees Centigrade, t minutes after the dish is placed in the refrigerator. Responding with complete sentences and appropriate units: A. What is the meaning of the derivative, D'(t)? B. What does D'(25) = 8 mean in this situation? C. Is D' (t) always negative? Or does it change sign? Explain.

Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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**Problem: Understanding the Temperature Change of a Dish in a Refrigerator**

A hot dish is placed in a refrigerator and then removed after eighty-five minutes. Suppose that the function \( D(t) \) represents the temperature of the dish, in degrees Centigrade, \( t \) minutes after the dish is placed in the refrigerator.

Responding with complete sentences and appropriate units:

**A. What is the meaning of the derivative, \( D'(t) \)?**

*[Response Box]*

**B. What does \( D'(25) = -8 \) mean in this situation?**

*[Response Box]*

**C. Is \( D'(t) \) always negative? Or does it change sign? Explain.**

*[Response Box]*
Transcribed Image Text:**Problem: Understanding the Temperature Change of a Dish in a Refrigerator** A hot dish is placed in a refrigerator and then removed after eighty-five minutes. Suppose that the function \( D(t) \) represents the temperature of the dish, in degrees Centigrade, \( t \) minutes after the dish is placed in the refrigerator. Responding with complete sentences and appropriate units: **A. What is the meaning of the derivative, \( D'(t) \)?** *[Response Box]* **B. What does \( D'(25) = -8 \) mean in this situation?** *[Response Box]* **C. Is \( D'(t) \) always negative? Or does it change sign? Explain.** *[Response Box]*
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