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I rent a Mother-In-Laws quarters that is on the side of my house. It has a private entrance.

If I'm concerned something has happened to the tenant, am I legally allowed to enter the building without giving notice?

Some background:
For the first time, my tenant is late on rent, and hasn't contacted me in any way which seems very unusual for her. Yesterday I texted once to remind about the rent, and a second time asking if they are okay once I noticed there was still mail from a few days ago in her mail box right by her door with no response. I also couldn't hear TV through the wall which I usually can, and her curtains were never opened which I notice she usually does during the day. The air conditioning also wasn't on all day, which is also unusual. She's elderly and I'm afraid she may have fallen or even worse. I'm planning on knocking on her door on my lunch break. If she does not answer the door, I'm trying to figure out if I can go ahead and enter the property and make sure everything is okay.

Most leases have a provision allowing a landlord to make entry without notice in an emergency, but the better course of action, as noted in a comment by @BlueDogRanch, is to call the police and ask them to make a "welfare check." You would ordinarily be permitted to cooperate with police by unlocking doors in furtherance of their welfare check.

The police are trained to do this properly in a way that properly balances the need to aid someone who is sick or ill, the need to preserve evidence if there was a death or crime that needs to be understood legally, and to protect the legitimate privacy interests of the tenant.

You are not. You could incur liability for failing to prevent death or aggravating injury, could be wrongfully implicated if physical evidence from you contaminates the scene or you destroy evidence showing the true cause, and could be sued for invading the tenant's privacy if it was found that you entry was unreasonable and that it wasn't really an emergency which is always easier to conclude with 20-20 hindsight.

As it is, your biggest potential source of liability is delaying in calling the police seeking a welfare check. They often respond quite quickly to these by the way, although it is not the very highest priority for law enforcement.

All usual disclaimers apply, IANAL, etc.

Apparently entry in CA should be done during office hours (9-5):

https://homeguides.sfgate.com/california-laws-unlawful-entry-residential-property-landlord-34199.html

That being said, most contracts and state law provide for landlords to provide notice and entry to perform maintenance.

A Landlord's Right of Entry

1. Does my landlord have the right to enter my apartment whenever he or she
wants?
A landlord or manager may enter rented premises while the tenant is living there without
advance notice in the case of emergency, such as a fire or serious water leak. And, of
course, a landlord may enter when a tenant gives permission.
Civil Code 1954
Under Civil Code 1954 [see below], the landlord may enter your unit without your
permission ONLY:
(1) in an emergency, like a fire or broken pipe, or
(2) upon reasonable advance notice, and then ONLY:
(A) to inspect, repair, or show the apartment,
(B) during normal business hours [presumably Mon.-Fri. 8AM-6PM]
(C) 24 hours is presumed to be sufficient notice
(D) You do not have to be home when they come, but the landlord is liable for
anything stolen or broken.
(D) The notice must identify a date and reasonable time range [like an hour] within
which the entry will occur
(E) The notice MUST be written [not oral or e-mail], except if a WRITTEN notice that
realtors will be showing the property is given, for the next 120 days only an oral telephonic
24 hour notice is required [business hour limit still applies]
(G) The right of entry can't be "abused", so that an open house, lock box, extended
repair, daily entry, or excessive range of entry time are probably all "abuses" which you
have the legal right to prevent.
The nature of the reasonableness of the notice seems to be to give you time to pick up the
place, secure pets, arrange to be there, or otherwise make ready for the visit. The law is not
clear, here, and the above is the best interpretation of what the law probably is.
2. What are examples of situations when a landlord may enter, but only after
giving the tenant reasonable notice?
Typically, a landlord has the right to enter rented premises after giving tenants reasonable
notice in order to make needed repairs (or assess the need for them) and to show the
property to prospective new tenants or purchasers. In addition, a landlord may enter rented
premises in instances of abandonment (that is, when the tenant moves out without
notifying the landlord) or by court order. A landlord may not enter just to check up on the
tenant.
3. Assuming it is not an emergency, but the landlord has a valid reason to enter --
for example, to make repairs -- what kind of notice is required?
Landlords are required to provide a specific amount of notice (usually 24 hours) before
entering a rental unit. In California, landlords must provide a reasonable amount of notice,
legally presumed to be 24 hours. Landlords can usually enter on shorter notice if it is
impracticable to provide the required amount of notice.
4. May a landlord enter a rental unit any time of day, as long as he's given the
required amount of notice?No. In most instances -- except emergencies, abandonment and invitation by tenant --
states allow a landlord to enter only at reasonable times, without setting specific hours and
days. California state law requires that landlords may enter only during normal business
hours. This would be Monday through Friday, between the hours of 8 a.m. and 5 p.m.
5. What are the landlord's options if a tenant refuses to allow entry even when a
landlord has given adequate notice and has a valid reason to enter?
A landlord should not force entry except when there is a true emergency, such as a fire or
gas leak. However, if a tenant is repeatedly unreasonable in denying the landlord access,
the landlord can legally enter anyway, during reasonable times, provided he does so in a
peaceful manner. However, in no case should the landlord enter if the tenant is present and
saying "stay out."
If a landlord has a serious conflict over access with an otherwise satisfactory tenant, a
sensible first step is to meet with the tenant to see if the problem can be resolved. Often,
neighborhood mediation programs will, for a low cost, help work out an agreement. If these
attempts at compromise don't work, a landlord can usually evict the tenant for violating the
lease or rental agreement, assuming it contains an appropriate right-of-entry provision.
6. What should a tenant do if a landlord repeatedly violates her privacy rights by
entering the rental unit with no good reason and/or advance notice?
Call the police. A landlord or manager who enter a tenant’s apartment without permission is
trespassing. Also, consult an attorney regarding taking legal action.