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3. A sample of paraffin wax is being heated in a laboratory. The tem- perature of the paraffin is given by H = f(t) degrees Celsius, where t represents time, in minutes (see graph to the right). (a) On what time intervals, if any, is the temperature of the paraffin increasing? (b) On what time intervals, if any, is the temperature of the paraffin decreasing? H t 1 2 3 4 5 6 7 8 9 10 (c) On what time intervals, if any, is the rate of temperature change increasing? Also explain how you know your answer is right. (d) On what time intervals, if any, is the rate of temperature change decreasing? Also explain how you know your answer is right.

3. A sample of paraffin wax is being heated in a laboratory. The tem- perature of the paraffin is given by H = f(t) degrees Celsius, where t represents time, in minutes (see graph to the right). (a) On what time intervals, if any, is the temperature of the paraffin increasing? (b) On what time intervals, if any, is the temperature of the paraffin decreasing? H t 1 2 3 4 5 6 7 8 9 10 (c) On what time intervals, if any, is the rate of temperature change increasing? Also explain how you know your answer is right. (d) On what time intervals, if any, is the rate of temperature change decreasing? Also explain how you know your answer is right.

Calculus: Early Transcendentals
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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**Question 3: Paraffin Wax Heating in the Laboratory** A sample of paraffin wax is being heated in a laboratory. The temperature of the paraffin is given by \( H = f(t) \) degrees Celsius, where \( t \) represents time, in minutes (see the graph to the right). **Graph Details:** - The graph displays the temperature \( H \) on the y-axis and time \( t \) on the x-axis. - Time \( t \) ranges from 0 to 10 minutes. - The curve starts below the x-axis, slopes upwards quickly between \( t = 1 \) and \( t = 3 \), flattens between \( t = 3 \) and \( t = 6 \), and steeply increases again from \( t = 6 \) to \( t = 10 \). **Questions:** (a) On what time intervals, if any, is the temperature of the paraffin increasing? (b) On what time intervals, if any, is the temperature of the paraffin decreasing? (c) On what time intervals, if any, is the rate of temperature change increasing? Also, **explain** how you know your answer is right. (d) On what time intervals, if any, is the rate of temperature change decreasing? Also, **explain** how you know your answer is right. **Graph Interpretation:** 1. **Temperature Increasing:** - Observing the graph, the temperature increases during the entire interval, as the graph is rising from \( t = 0 \) to \( t = 10 \). 2. **Temperature Decreasing:** - There are no intervals where the temperature decreases, as the graph shows a continuous upward slope. 3. **Rate of Temperature Change Increasing:** - Occurs where the graph's slope is getting steeper, specifically from \( t = 0 \) to \( t = 3 \) and \( t = 6 \) to \( t = 10 \). - Explanation: The steepness of the graph indicates the rate of change is increasing. 4. **Rate of Temperature Change Decreasing:** - Occurs where the graph's slope is flattening, from \( t = 3 \) to \( t = 6 \). - Explanation: The flattening of the graph suggests the rate of temperature change is decreasing.
Transcribed Image Text:**Question 3: Paraffin Wax Heating in the Laboratory** A sample of paraffin wax is being heated in a laboratory. The temperature of the paraffin is given by \( H = f(t) \) degrees Celsius, where \( t \) represents time, in minutes (see the graph to the right). **Graph Details:** - The graph displays the temperature \( H \) on the y-axis and time \( t \) on the x-axis. - Time \( t \) ranges from 0 to 10 minutes. - The curve starts below the x-axis, slopes upwards quickly between \( t = 1 \) and \( t = 3 \), flattens between \( t = 3 \) and \( t = 6 \), and steeply increases again from \( t = 6 \) to \( t = 10 \). **Questions:** (a) On what time intervals, if any, is the temperature of the paraffin increasing? (b) On what time intervals, if any, is the temperature of the paraffin decreasing? (c) On what time intervals, if any, is the rate of temperature change increasing? Also, **explain** how you know your answer is right. (d) On what time intervals, if any, is the rate of temperature change decreasing? Also, **explain** how you know your answer is right. **Graph Interpretation:** 1. **Temperature Increasing:** - Observing the graph, the temperature increases during the entire interval, as the graph is rising from \( t = 0 \) to \( t = 10 \). 2. **Temperature Decreasing:** - There are no intervals where the temperature decreases, as the graph shows a continuous upward slope. 3. **Rate of Temperature Change Increasing:** - Occurs where the graph's slope is getting steeper, specifically from \( t = 0 \) to \( t = 3 \) and \( t = 6 \) to \( t = 10 \). - Explanation: The steepness of the graph indicates the rate of change is increasing. 4. **Rate of Temperature Change Decreasing:** - Occurs where the graph's slope is flattening, from \( t = 3 \) to \( t = 6 \). - Explanation: The flattening of the graph suggests the rate of temperature change is decreasing.
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