Let be an open interval, let be differentiable on , and suppose exists at . Show that Give an example where this limit exists, but the function does not have a second derivative at .
Last edited by CrazyCat87; April 18th 2010 at 04:43 PM.
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Originally Posted by CrazyCat87 Let be an open interval, let [tex]f:I \rightarrow \mathbb{R} be differentiable on , and suppose exists at . Show that Give an example where this limit exists, but the function does not have a second derivative at . Use Taylor polynomials of order 2 around : Now add both eq's above and solve for and let Tonio
Does represent the remainder term of the function? I'm confused as to why it disappears..
Originally Posted by CrazyCat87 Does represent the remainder term of the function? I'm confused as to why it disappears.. It doesn't disappear: when we add the corresponding eq's we get , and when this, of course, vanishes in the limit... Tonio
ah yes
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