How do I know if my furnace heat exchanger is cracked

You cannot safely tell if a heat exchanger is cracked without professional equipment because cracks form inside the metal chambers and are usually invisible from outside. However, warning signs include a burning or acrid plastic smell during heating season, visible rust stains on the furnace exterior, or moisture pooling around the base.
Immediate safety step
If you smell an acrid burning odor when heat runs, turn off the furnace right away and open windows. Install a battery powered carbon monoxide detector in your bedroom and living area if you don't have one. Call a technician the same day. Do not ignore this.
Why replacement is the only option
Heat exchangers transfer heat from combustion into your home's air. A crack allows carbon monoxide to enter your ductwork. Welding or patching is not safe or legal because the exchanger will crack again under pressure and temperature cycling. The only safe repair is furnace replacement. Your technician can confirm a crack with a video inspection scope for around fifty to one hundred dollars if you need confirmation before committing to replacement.