Functions with Corners
Author: Jamie Mulholland
Date: September 16, 2008

Tangent lines don't necessarily exist at every point on a graph.  Below there are some examples of functions which have "corners" - sharp turns where tangent lines cannot exist.

Functions with 'corners'

f(x)=|x|

Tangent line does not exist at (0,0) since
there is a 'corner' there.

Tangent line does not exist at (2,3) since
there is a 'corner' there.

Slide to change graphs

f(x) = abs(x)
g_1(x) = -(x - 2.0)^(2.0 / 3.0) + 2.0
g_2(x) = 1.0 / (x + 4.0) + 11.0 / 6.0
g = If(x ≤ 2.0, g_2, g_1)
toggle = 0 (slider from 0 to 1, step 1)
A = Point(g)
a = Tangent(A, g)