hi guys, what is the relationship between y^2 = f(x) and y = f(x)?
Oh, you don't really mean y=f(x), and y2=f(x) do you? I think what you mean to say is if we're given a function f(x), then what is the relation between the function f(x), and the function (f(x))2.let's say we are given a function y=f(x), what is relationship between it and y^2 =f(x)?
for example, if y=f(x) have a maximum point at (a,b), will y^2=f(x) have a maximum point at(a,b) too?
i hope i make my question clear.
That depends on whether f(a) is positive or negative. If f(a) is negative and a minimum, (f(a))^2 may be a maximum (e.g., if f(x) is the cosine function, then f(pi) is a minimum put (f(pi))^2 is a maximum).I think it should be fairly easy to show that if f has a min at x=a then so does f2, and the same if f has a max at x=a, but I'm a bit too tired to try a proof of that at the moment.