Wikipedia:Reference desk/Archives/Mathematics/2008 January 20
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January 20
[edit]Quick calculus question
[edit]In a problem I'm trying to solve, I am shown the graph of the derivative of a function g. The derivative is continuous on the shown interval, which includes the x-value a. Since a y-value on the graph of the derivative is given for the x-value a, I can infer that g is differentiable at x = a. But I don't know how to infer from the graph of g‘ whether g is continuous at x = a. Does differentiability imply continuity? Thanks, anon. —Preceding unsigned comment added by 70.18.17.227 (talk) 05:00, 20 January 2008 (UTC)
- You bet it does... the section on "Continuity and differentiability" at Derivative provides an excellent explanation on why this is so, so I'll omit it here, for the sake of not being redundant. :) --Kinu t/c 05:11, 20 January 2008 (UTC)
- Perfect. Thanks a bunch. —Preceding unsigned comment added by 70.19.20.251 (talk) 04:38, 22 January 2008 (UTC)