[DOC] [TLE] Vertical Tangents and Cusps - SOS Math [PAR] In the definition of the slope, vertical lines were excluded. It is customary not to 
assign a ... The graph of a function f(x) has a vertical tangent at the point (x0,f(x0)) 
if and only if ... In fact, we have left and right derivatives with ... All rights reserved. [DOC] [TLE] Differentiability at a point (old) | Differentiability | Taking derivatives ... [PAR] Aug 22, 2013 - 4 minAn older video where Sal finds the points on the graph of a function where the  function isn't ... [DOC] [TLE] 9.2 Non-Differentiable Functions [PAR] After all, differentiating is finding the slope of the line it looks like (the tangent line 
... Also when the tangent line is straight vertical the derivative would be infinite 
and ... The function's graph has a kink, like the letter V has. ... Now you have seen 
just about everything there is to say about differentiating functions of one variable
. [DOC] [TLE] Differentiable function - Wikipedia [PAR] In calculus (a branch of mathematics), a differentiable function of one real 
variable is a function whose derivative exists at each point in its domain. As a 
result, the graph of a differentiable function must have a (non-vertical) tangent 
line ... Most functions that occur in practice have derivatives at all points or at 
almost every... [DOC] [TLE] Vertical line test - Wikipedia [PAR] In mathematics, the vertical line test is a visual way to determine if a curve is a 
graph of a function or not. A function can only have one output, y, for each unique 
input, x. ... one value of y, and so, the curve does not represent a function. If all 
vertical lines intersect a curve at most once then the curve represents a function. [DOC] [TLE] 2.4 CONTINUOUS FUNCTIONS - Saylor [PAR] and at every point shown except at 2, 3, and 4. ... A function is not continuous at a 
point if its graph has a hole or break at that point. ... 1, at a = 1, all 3 conditions are 
satisfied, and f is continuous at 1. .... 8): if one value of the continuous function is 
below the line and another value of .... y = f(x), and the vertical line at x (Fig. 21). [DOC] [TLE] MATH 221 FIRST SEMESTER CALCULUS [PAR] A shorter, but not quite perfect derivation of the Quotient Rule. 54. 24.6. ..... 1.2  
Which of the following fractions have finite decimal expansions? a = 2. 3. , b = .... 
The expression 1/x2 can be computed for all real numbers x except x = 0 since 
this leads to ... The graph of a function intersects vertical lines in at most one point
,. [DOC] [TLE] What is a Linear Function? - Boundless [PAR] The graph of a linear function is a straight line, but a vertical line is not the graph 
... the definition of a function - for each input ( $x$ ) there is exactly one output ( $y
$ ). ... value of $4$ for all points on the line, but would have different output values
, .... Except where noted, content and user contributions on this site are licensed... [DOC] [TLE] Math Tutor - Derivatives - Theory - Derivative [PAR] Then we look at derivative as a function and show some basic properties. ... Can 
we draw a tangent line to this graph at the given point? .... Geometrically, the 
tangent line to the graph at that point is vertical. ... One-sided derivative has the 
same properties as the usual derivative, all theorems that use derivative will also 
work... [DOC] [TLE] Find vertical tangent lines [PAR] The curve y = f(x) has a vertical tangent line at the point (a, f(a)) if. (i) f(x) is a ... 
Example 1 Find all the points on the graph y = x1/2 x3/2 where the tangent line 
is either ... One can also use quotient rule to compute the derivative: y = . [DOC] [TLE] Continuity and Differentiability [PAR] miscellaneous on

Question: On a graph, the derivative of a function is this, which all lines except vertical ones have
Answer: a slope