Problem Three: 2000-2001
Calculus I (AB) and II (BC): Continuity,
Schmontinuity
Give the value of M, in terms
of a, b, and c, which makes the function f(x)
continuous if
Difficulty Rating:


Solution:
The rule which defines this function changes
at x =
1. If the function
is to be continuous, the two pieces of the graph must meet there. Thus,
both functions must have the same output (height) when x =
1.
Plug in x =
1 and solve
for M:
Substituting this ugly fraction for M results in a
value of a
b + c
for both pieces of the function when x =
1.
