For what value of the constant c is the function f continuous on (−∞, ∞)? f(x) = (cx2 + 9, if x < 4) (x^3 − cx, if x ≥ 4)

Answer 1

To be continuous, f(4) must give the same value whether you approach 4 from the left or from the right.

c(4²) + 9 = 4³ - c(4)

16c + 9 = 64 - 4c

20c = 55

c = 55/20 = 11/4