Vertical Tangent
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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...
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.
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