Suppose that f (x) is known to be continuous, and the graph of ƒ (x) on [a, b] has no • corners • cusps • points of vertical tangency • infinite oscillations Can we conclude that f (x) is differentiable on (a, b)? O No Yes

Linear Algebra: A Modern Introduction
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ISBN:9781285463247
Author:David Poole
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Chapter6: Vector Spaces
Section6.5: The Kernel And Range Of A Linear Transformation
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Suppose that f (x) is known to be continuous, and the graph of ƒ (x) on [a, b] has no
• corners
• cusps
• points of vertical tangency
infinite oscillations
Can we conclude that f (x) is differentiable on (a, b)?
O No
Yes
Transcribed Image Text:Suppose that f (x) is known to be continuous, and the graph of ƒ (x) on [a, b] has no • corners • cusps • points of vertical tangency infinite oscillations Can we conclude that f (x) is differentiable on (a, b)? O No Yes
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