Tutorial Exercise cx² + 9x if x < 4 Let f(x) = x³ - cx if x 24. For what value of the constant c is the function of continuous on (-00, 00)? Step 1 Recall that a function f is continuous at a number a if the following holds. lim f(x) = f(a) x→a We are given the following. if x < 4 f(x) = x³ - cx if x 24 We note that for all values of the constant c the function f is continuous on both (-[infinity]0, 4) and (4, [infinity]o). The only case that we need to consider is when x = 4. For the function f to be continuous on (-[infinity]0, [infinity]o), we need to ensure that there is not a discontinuity at x = 4. To do so, we must determine the value of c such that the following holds. lim f(x) = lim f(x) X-4 X-4+ Find the following limits. limf(x) lim (cx² + 9x) x-4 X-4 = X lim (x³ - cx) lim f(x) x→4+ x+4+