What exactly does it mean for a function to be differentiable on an interval?

Question

anonymous · Answer

It means it actually has a derivative for those values of x.

For example, $y =|x|$ has no derivative at x = 0.

amistre64 · Answer

a derivative is a limit process, and in order to be differentiable on an interval; it has to have a definable limit for each x in the interval as SACs example portrays

anonymous · Answer

In the problem, would the answer only be j(x) then? I'm still kind of confused

loser66 · Answer

for "what exactly does it mean for a function to be differentiable" http://web.mit.edu/wwmath/calculus/differentiation/definition.html

amistre64 · Answer

take the derivatives of the setups, and test them out.

j(x) is an obvious one of course

amistre64 · Answer

b has a vertical asymptote in the interval at x=4, so it most likely is bad

amistre64 · Answer

if the others do not have the same derivative value at their "breaking points" then they would be out as well

amistre64 · Answer

i spose contuity might play a part as well :/

psymon · Answer

A lot of the time its pretty obvious to determine, its just the definitions and the whole limit process stuff can make it seem confusing. In the end, you're looking to avoid breaks in continuity, sharp points, and vertical lines. 

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