Let f(x) = x³ − x² + x + 1 and g(x) = max{f(t): 0 ≤ t ≤ x} for 0 ≤ x ≤ 1, then g(x) is not differentiable at x = 1/3. True or False: g is discontinuous at x = 1/3.

Let f(x) = x³ − x² + x + 1 and g(x) = max{f(t): 0 ≤ t ≤ x} for 0 ≤ x ≤ 1, then g(x) is not differentiable at x = 1/3. True or False: g is discontinuous at x = 1/3.

• A. False, g is continuous everywhere
• B. True, jump discontinuity
• C. False, removable discontinuity
• D. True, infinite discontinuity

Answer: A) False, g is continuous everywhere

Explanation: g(x) is always continuous as the maximum function of a continuous function. It may not be differentiable where f stops being the maximum, but it remains continuous.