For what value of the constant c is the function f continuous on (−[infinity], [infinity])?f(x) = leftbrace2.gif cx2 + 9x if x < 4
x3 − cx if x ≥ 4
Note that f is continuous on (−[infinity], 6) and (6, [infinity]). For the function to be continuous on (−[infinity], [infinity]), we need to ensure that as x approaches 6, the left and right limits match.
First we find the left limit.
lim x→4−f(x) = lim x→4− (cx2 + 9x) =
Next, we find the right limit. lim x→4+f(x) = lim x→4+ (x3 − cx) =