What is the function derivative?

What an explicit formula for a function g(x) has a derivative everywhere has 2 critical points 0 rel extrema?

• f(x) = x^4 has a derivative everywhere, has a critical point at x = 0 but has no relative extrema.Give an explicit formula for a function g(x) that has a derivative everywhere, has exactly two critical points

• Answer:

  You've mis-stated the problem somehow. The question title you posted does not parse into English sentences, but at least the text gives the full version. However, the initial statement is both incorrect (x^4 has a very distinct relative extreme at (0,0) ) and immaterial, as any polynomial function of even degree *must* have at least one extreme. I believe that what you need is a cubic function. I suggest that you build it form factors, so you can guarantee that it has three roots, which necessitates two relative extrema. In general, g(x) = (x-a)(x-b)(x-c) will have three roots and two relative extrema whenever a, b, and c are different values. I suggest -1, 0, and 1 to make things simple.