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Thank you first for your attention to this question.

The thing goes like this:

I was taught that this phrase had better do was used to ask somebody to do something, and it was good to do so.

Later I learnt that this phrase was kind of strong, and it suggested something like warning.

So my question is when I can use this phrase?

For example, if I just want someone to something instead of doing otherwise, nothing serious, just something small, trivial, can I use had better do...?

And, if I were a customer service, could I use you'd better do... when I explain to a customer how to use a product? Suppose that the thing I explain to the customer is not dangerous and it won't cause life and property damage. And how about it is dangerous?

By the way, are those words marked red grammatically correct?

Thanks in advance. I'm sorry this is long and maybe complicated.
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First, let's check those expressions in red.
erebreakinstead of doing otherwise
Correct.
erebreak if I were a customer service, could I use you'd better do..
No.

if I worked in customer service or if I were serving a customer.
____________

Now for the question itself.
erebreakLater I learnt that this phrase was kind of strong, and it suggested something like warning.
That's correct.
erebreakSuppose that the thing I explain to the customer is not dangerous and it won't cause life and property damage. And how about it is dangerous?
I don't understand what you are trying to say. Let's just get back to the main question.

Use "You'd better" ("You had better") for warnings. You'd better be on time, or we'll leave without you.

To advise a customer, use "It would be better if you" or "I think it would be better if you" or "I would advise you to" or "I would recommend that you". You need to provide a more exact situation. Without the exact context between you and your customer it's hard to say what the best phrases might be.

CJ
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 CalifJim's reply was promoted to an answer.