Could you give me some hints to solve the problem?

Problem 5. A nancial expert is giving the following advice: \"It is rarely optimal to exercise an American call option on a non-dividend paying stock early. However, when the underlying stock hits an all time high and then does not go up much over the next month, early exercise is optimal because the chance that the stock goes up in price any more is very small. In this type of situation, you can do nothing but lose by not exercising." Do you agree with the advise of the nancial expert? Why