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The total amount of rainfall, in centimeters, as a function of time, in days, is modeled by the function f, where g is a differentiable function. The data in the table gives values of g(t) at selected values of t. 15 f(t)= t g(t) t for 2st<8 for 8 st≤14 8 10 12 14 g(t) 1.875 1.433 1.115 1.004 Part A: What is the average rate of change of the amount of rainfall from day 8 to day 14, according to function f? Part B: Use the data in the table to approximate f '(13). Show your work. Part C: Is f a continuous function from 2 sts 14? Explain.

The total amount of rainfall, in centimeters, as a function of time, in days, is modeled by the function f, where g is a differentiable function. The data in the table gives values of g(t) at selected values of t. 15 f(t)= t g(t) t for 2st<8 for 8 st≤14 8 10 12 14 g(t) 1.875 1.433 1.115 1.004 Part A: What is the average rate of change of the amount of rainfall from day 8 to day 14, according to function f? Part B: Use the data in the table to approximate f '(13). Show your work. Part C: Is f a continuous function from 2 sts 14? Explain.

College Algebra
College Algebra
7th Edition
ISBN:9781305115545
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:James Stewart, Lothar Redlin, Saleem Watson
Chapter2: Functions
Section2.4: Average Rate Of Change Of A Function
Problem 4E
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The total amount of rainfall, in centimeters, as a function of time, in days, is modeled by the function f, where g is a differentiable function. The data in the table gives values of g(t) at selected values of t. f(t) = 15 t g(t) 8 10 12 14 g(t) 1.875 1.433 1.115 1.004 2≤t<8 for for 8≤t≤14 Part A: What is the average rate of change of the amount of rainfall from day 8 to day 14, according to function f ? Part B: Use the data in the table to approximate f'(13). Show your work. Part C: Is f a continuous function from 2 ≤ t ≤ 14? Explain. Part D:Find f'(5) using the limit definition of the derivative. Show your work and explain its meaning.
Transcribed Image Text:The total amount of rainfall, in centimeters, as a function of time, in days, is modeled by the function f, where g is a differentiable function. The data in the table gives values of g(t) at selected values of t. f(t) = 15 t g(t) 8 10 12 14 g(t) 1.875 1.433 1.115 1.004 2≤t<8 for for 8≤t≤14 Part A: What is the average rate of change of the amount of rainfall from day 8 to day 14, according to function f ? Part B: Use the data in the table to approximate f'(13). Show your work. Part C: Is f a continuous function from 2 ≤ t ≤ 14? Explain. Part D:Find f'(5) using the limit definition of the derivative. Show your work and explain its meaning.
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