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Vertical Tangent
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Geliefert zwischen Mi., 28.01.2026 und Do., 29.01.2026
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High Quality Content by WIKIPEDIA articles! In mathematics, 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.A function has a vertical tangent at x = a if the difference quotient used to define the derivative has infinite limit: lim{hto 0}frac{f(a+h) - f(a)}{h} = {+infty}quadtext{or}quadlim{hto 0}frac{f(a+h) - f(a)}{h} = {-infty}. 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 has a vertical tangent at x = a if the derivative of 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 lim{xto a} f'(x) = {+infty}text{,} then must have an upward-sloping vertical tangent at x = a. Similarly, if lim{xto a} f'(x) = {-infty}text{,} then must have an downward-sloping vertical tangent at x = a. In these situations, the vertical tangent to appears as a vertical asymptote on the graph of the derivative.
Weitere Informationen
- Allgemeine Informationen
- GTIN 09786131159145
- Editor Lambert M. Surhone, Miriam T. Timpledon, Susan F. Marseken
- EAN 9786131159145
- Format Fachbuch
- Titel Vertical Tangent
- Herausgeber Betascript Publishing
- Anzahl Seiten 92
- Genre Mathematik
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