Question

Show that the function defined as follows, is continuous at x = 1, x = 2 but not differentiable at x = 2. f(x) = {3x - 2, 0 < x ≤ 1 and 2x² - x, 1 < x ≤ 2 and 5x - 4, x > 2}

Answer 1

Given  that,

Firstly, we show the continuity of above function at x = 1 and at x = 2

Hence, f(x) is continuous at all indicated points. Now, let us verify differentiability of the given function at x = 2

Hence, f(x) is continuous at x = 1 and x = 2 but not differentiable at x = 2