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In mathematics, particularly calculus, a vertical tangent is tangent line that is vertical. Because a vertical line has infinite slope, a function whose graph has a vertical tangent is not differentiable at the point of tangency. == Limit definition == A function ƒ has a vertical tangent at ''x'' = ''a'' if the difference quotient used to define the derivative has infinite limit: : The first case corresponds to an upward-sloping vertical tangent, and the second case to a downward-sloping vertical tangent. Informally speaking, the graph of ƒ has a vertical tangent at ''x'' = ''a'' if the derivative of ƒ at ''a'' is either positive or negative infinity. For a continuous function, it is often possible to detect a vertical tangent by taking the limit of the derivative. If : then ƒ must have an upward-sloping vertical tangent at ''x'' = ''a''. Similarly, if : then ƒ must have a downward-sloping vertical tangent at ''x'' = ''a''. In these situations, the vertical tangent to ƒ appears as a vertical asymptote on the graph of the derivative. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Vertical tangent」の詳細全文を読む スポンサード リンク
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