Question

For what value of the constant c is the function f continuous on (−∞, ∞)?
f(x) =

cx2 + 4x if x < 3
x3 − cx if x ≥ 3

Answer 1

There's some font mangling from your copy/paste, but if I read it right,

f(x) =
cx^2 if x < 3
x^3 if x >= 3

limit(x->3-) = 9c
limit(x->3+) = 27

so, if c=3 the two branches join at (3,27)