Question

The function f(x) = [(ax(x - 1) + b, when x < 1), (x - 1, when 1≤ x ≤ 3), (px² + qx + 2, when x > 3)

Find the values of the constants a, b, p, q so that

(i) f(x) is continuous for all x

(ii) f'(1) does not exist

(iii) f'(x) is continuous at x = 3

Answer 1

f(x) is continuous at x = 1