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Deflection

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Austim,(Follows our discussion for the threade that disappeared)
Thank you for the response to my previous thread i very well understand that d2y/dx2 is not zero at the ends.Is it that, the tangents drawn at x=0 and x=l/2 cannot meet because there is a point of inflection between the two?So to get d2y/dx2 diagramettically (say) at x=0, the tangents should be drawn between x=0 and the inflection point to get d2y/dx2 ? Right?
As you mentioned in the previous thread, that tangents should be drawn at close points else it is a chord,but say when we find the slope of a cantilever beam(free end) with a point load at the end by moment area theorem we draw tangents at x=0 and at x=l and get the angle between the two?Right
 
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