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OpenStudy (canada907cat):
Where is the graph below not differentiable and why? A) f(x) is not differentiable at x = 1 because f(x) has a cusp at x = 1. B) f(x) is not differentiable at x = 1 because f(x) has a corner at x = 1. C) f(x) is not differentiable at x = 1 because f(x) is discontinuous at x = 1. D) f(x) is not differentiable at x = 1 because f(x) has a vertical tangent at x = 1.
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OpenStudy (canada907cat):
OpenStudy (australopithecus):
Well the graph is continuous but look at the definition of a derivative, the limit would not exist at the point where there is a corner
OpenStudy (australopithecus):
OpenStudy (australopithecus):
Also note that this graph is clearly continuous
OpenStudy (canada907cat):
Ah I see it is a corner. I couldn't tell if it was a corner or a cusp so thank you for clearing that up for me.
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OpenStudy (australopithecus):
no problem
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