Given the function f(x) = {2ª 2x x < 2 x > 2 which statement is FALSE at x=2? O The derivative from the left of f at x=2 is 2. O The derivative from the right of f at x=2 is 4. Of is continuous, but not differentiable at x=2. Of is differentiable, but not continuous at x=2.

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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Given the function
2x
x < 2
f(x) =
x² x > 2
which statement is FALSE at x=2?
The derivative from the left of fat x=2 is 2.
The derivative from the right of fat x=2 is 4.
Of is continuous, but not differentiable at x=2.
f is differentiable, but not continuous at x=2.
OOO
Transcribed Image Text:Given the function 2x x < 2 f(x) = x² x > 2 which statement is FALSE at x=2? The derivative from the left of fat x=2 is 2. The derivative from the right of fat x=2 is 4. Of is continuous, but not differentiable at x=2. f is differentiable, but not continuous at x=2. OOO
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