Critical points, global max/min?

Question

For each of the following, come up with a function that satisfies all the given conditions.
(a) function with a global max and global min on a closed interval.
(b) A function with a global max and no global min.
(c) A function with no global max and no global min.
(d) A function with no local max/min but with a global max and global min on a closed interval.
(e) A function with a critical point but no global max/min.
(f) A discontinuous function with a global max and global min.
(g) A function with exactly two critical points, a global max and a global min.
(h) A function with exactly two critical points but no global max or min.

Answer 1

I think you'll need to make some sketches and play around with functions to see what you can come up with. Also double-check the definitions in YOUR book, because there can be differences from book to book. For example, sin(x) is a function with a global min (-1) and global max (+1) on a closed interval [-pi/2, pi/2], but it's possible your book (or teacher) is looking for what some people call "strict" global maxima and minima, then that would be incorrect because there are infinitely many of them. In that case you could multiply by a function that decreases away from the origin, such as exp(-x^2), and that would turn those into a strict global minimum and maximum.



The Wikipedia entry on maxima and minima may be useful to you.



You might also play around with the signum function (-1:x<0;+1:x>0) shifted and differenced to make a global maximum and minimum for a discontinuous function.

Answer 2

Do your own homework man. Calc 1 is cake.

Answer 3

This doesn't have to do with global warming.

y=x will satisfy c

Answer 4

My friend Tom is an expert on cheating on tests. Do your test.