Step 1: Check Continuity For f(x) = {g(x), x < a; h(x), x >= a}: compute lim(x->a-) g(x), lim(x->a+) h(x), and f(a) = h(a). All three must be equal.

Step 2: Check Differentiability Left derivative: lim(h->0-) [f(a+h)-f(a)]/h = g'(a) (usually) Right derivative: lim(h->0+) [f(a+h)-f(a)]/h = h'(a) (usually) Both must be equal for f'(a) to exist.

Step 3: If finding parameters, set up equations:

• Continuity gives one equation
• Equal derivatives gives another equation

Important: Even if g'(x) and h'(x) have limits at a, you should verify using the definition of derivative, not just lim f'(x).