Question

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.

Answer 1

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

Answer 2

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

Answer 3

Also note that this graph is clearly continuous

Answer 4

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.

Answer 5

no problem