I hope someone can help. I'm hoping that someone help me understand combined function characteristics with the following examples:

**1. y=2^x-x^3**would this function not have a relative maximum at x = 0.59? Would it also have a minimum at x = 8.177?

**2. y = sin(2pix) - 2sin(pix)**my textbook says that the zero/x-intercept for this function is

*k*. Which doesn't make any sense to me. Can someone please tell me whether this is correct to think that the zero is

*k*?

**3. y = sin(2pix) + 2 + (1/x)**my textbook says that this function has zeros that are changing at irregular intervals - however, I personally don't see where the function experiences any zeros in the first place. Am I understanding this correctly?

**4. y = sin(2pix) + 2 + (1/x)**The textbook is also saying for the same function as the one above that the maximum and minimum values are at irregular intervals. I don't see how this is possible. Do you think that my textbook is referring to local maximum or minimum values?

I know these are a lot of questions, but there wasn't a lot of information online that I could find to help me. Again, I really hope someone can help!

Sincerely,

Olivia