Question

Let f(x) = x³ - x² + 1 and

g(x) = max{f(t); 0 ≤ t ≤ x} 0 ≤ x ≤ 1

g(x) = 3 - x, 1 < x ≤ 2

Discuss the continuity and differentiability of the function g(x ) in the interval (0, 2).

Answer 1

Given, f(x) = x³ - x² + 1