Question

Let f(x) = x³ – 9x² + 15x + 6 and g(x) = {min f(t); 0 ≤ t ≤ x, 0 ≤ x ≤ 6, x - 18; x > 6 Draw the graph of g(x) and discuss the continuity and differentiability of g(x).

Answer 1

f(x) is discontinuous at x = 6 and non-differentiable at x = (9 - √21)/2, 6