Question

For what value of the constant c is the function f continuous on (−, )?
f(x) =
cx2 + 2x if x < 3
x3 − cx if x ≥ 3

Answer 1

Since \(3\) is the point of potential discontinuity, you want to let \(x=3\).

Answer 2

You want both ends to meet, so set them equal and solve for \(c\).