Question

Find the values of a and b, if. the function f defined by f(x) = {x² + 3x + a, x ≤ 1 and bx + 2, x > 1} is differentiable at x = 1

Answer 1

Given  that,

is differentiable at x = 1.

Clearly, for Rf'(1) to exist b - a - 2 should be equal to 0, i.e.

b - a - 2 = 0..........(ii)