as adjective
to turn a 形容詞 into an adjective, just make い→く
強く叩く To strike someone strongly
negative form (〜ない) is also a 形容詞
And hence follows the same rules
子供は泣かなくなる Children become non-criers; Children don't cry anymore
ケーキを食べなくなりました It has become so that I don't eat cake ; I don't eat cake anymore
with する・なる
indicate something changing/becoming an い-adjective, you conjugate it as 〜く.
Note that no extra に is necessary, also when used with なる.
涼しくなった It has become cool
値段を安くした I made the price cheap.
去年から背が高くなったね You have grown since last year, haven't you?