It took 16 seconds for a mercury thermometer to rise from - 20°C to 100°C when it was taken from a freezer and placed in boiling water. Show that somewhere along the way the mercury was rising at the rate of 7.5°C/second. Use the Mean Value Theorem. Suppose y = f(x) is continuous on a closed interval [a,b] and differentiable on the interval's interior (a,b). Then there is at least one point c in (a,b) at which the following is true. f(b) – f(a) =f'(c) b-a If f(t) is the function that represents the temperature shown on the thermometer after t seconds, what is the closed interval for this application? Assume that the thermometer is at the starting temperature at time t= 0.

Calculus: Early Transcendentals
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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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It took 16 seconds for a mercury thermometer to rise from - 20°C to 100°C when it was taken from a freezer and placed in boiling water. Show that somewhere along
the way the mercury was rising at the rate of 7.5°C/second.
Use the Mean Value Theorem.
Suppose y = f(x) is continuous on a closed interval [a,b] and differentiable on the interval's interior (a,b). Then there is at least one point c in (a,b) at which the following
is true.
f(b) – f(a)
=f'(c)
b-a
If f(t) is the function that represents the temperature shown on the thermometer after t seconds, what is the closed interval for this application? Assume that the
thermometer is at the starting temperature at time t= 0.
(Type your answer in interval notation.)
Transcribed Image Text:It took 16 seconds for a mercury thermometer to rise from - 20°C to 100°C when it was taken from a freezer and placed in boiling water. Show that somewhere along the way the mercury was rising at the rate of 7.5°C/second. Use the Mean Value Theorem. Suppose y = f(x) is continuous on a closed interval [a,b] and differentiable on the interval's interior (a,b). Then there is at least one point c in (a,b) at which the following is true. f(b) – f(a) =f'(c) b-a If f(t) is the function that represents the temperature shown on the thermometer after t seconds, what is the closed interval for this application? Assume that the thermometer is at the starting temperature at time t= 0. (Type your answer in interval notation.)
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