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Analyze the function f(x) = {. No 12 -10 if z < 6 +7 if x ≥ 6 √6 Your classmates may be analyzing different functions, so in your initial post in Brightspace be sure to specify the function that you are analyzing. I Part 1: Is f(z) continuous at z = 6? Explain why or why not in your Discussion post Yes No Hint: In order for f (z) to be continuous at x = 6, the limits of f (2) from the left and from the right must both exist and be equal to f (6). Part 2: Is f(z) differentiable at z = 6? Explain why or why not in your Discussion post. Yes Hint: Similarly to continuity, in order for f(x) to be differentiable at x = 6, f (x) must be continuous at x = 6 and the limits of the difference quotient ƒ(6+h)-f(6) from the left and from the right must both exist and be equal to each other. h

Analyze the function f(x) = {. No 12 -10 if z < 6 +7 if x ≥ 6 √6 Your classmates may be analyzing different functions, so in your initial post in Brightspace be sure to specify the function that you are analyzing. I Part 1: Is f(z) continuous at z = 6? Explain why or why not in your Discussion post Yes No Hint: In order for f (z) to be continuous at x = 6, the limits of f (2) from the left and from the right must both exist and be equal to f (6). Part 2: Is f(z) differentiable at z = 6? Explain why or why not in your Discussion post. Yes Hint: Similarly to continuity, in order for f(x) to be differentiable at x = 6, f (x) must be continuous at x = 6 and the limits of the difference quotient ƒ(6+h)-f(6) from the left and from the right must both exist and be equal to each other. h

College Algebra (MindTap Course List)
College Algebra (MindTap Course List)
12th Edition
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:R. David Gustafson, Jeff Hughes
Chapter3: Functions
Section3.3: More On Functions; Piecewise-defined Functions
Problem 99E: Determine if the statemment is true or false. If the statement is false, then correct it and make it...
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Analyze the function f(x) = {. No 12 -10 if z < 6 +7 if x ≥ 6 √6 Your classmates may be analyzing different functions, so in your initial post in Brightspace be sure to specify the function that you are analyzing. I Part 1: Is f(z) continuous at z = 6? Explain why or why not in your Discussion post Yes No Hint: In order for f (z) to be continuous at x = 6, the limits of f (2) from the left and from the right must both exist and be equal to f (6). Part 2: Is f(z) differentiable at z = 6? Explain why or why not in your Discussion post. Yes Hint: Similarly to continuity, in order for f(x) to be differentiable at x = 6, f (x) must be continuous at x = 6 and the limits of the difference quotient ƒ(6+h)-f(6) from the left and from the right must both exist and be equal to each other. h
Transcribed Image Text:Analyze the function f(x) = {. No 12 -10 if z < 6 +7 if x ≥ 6 √6 Your classmates may be analyzing different functions, so in your initial post in Brightspace be sure to specify the function that you are analyzing. I Part 1: Is f(z) continuous at z = 6? Explain why or why not in your Discussion post Yes No Hint: In order for f (z) to be continuous at x = 6, the limits of f (2) from the left and from the right must both exist and be equal to f (6). Part 2: Is f(z) differentiable at z = 6? Explain why or why not in your Discussion post. Yes Hint: Similarly to continuity, in order for f(x) to be differentiable at x = 6, f (x) must be continuous at x = 6 and the limits of the difference quotient ƒ(6+h)-f(6) from the left and from the right must both exist and be equal to each other. h
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