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Mathematics 21 Online
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.

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):

http://www.sosmath.com/calculus/diff/der09/Image03.gif

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.

OpenStudy (australopithecus):

no problem

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