Question

true or false... the function f(x)=2x^3+x has no max or min

Answer 1

you need to specify a domain for the function.

Answer 2

there is no set domain given

Answer 3

For example, on the domain [0,1] it most definitely has both.

Answer 4

So that means we're considering it on its maximal domain, which is the entire real line.

Let me ask you, if this function did have a local max or min, what could we say about the first derivative f'(x) at those points?

Answer 5

something about being greater than zero right?

Answer 6

This is one of the most basic properties of a derivative. If p is a local max or min of a differentiable function, then f'(p) = 0.

Answer 7

Does that look familiar?

Answer 8

yes it does... trying to find it in my book

Answer 9

Really, really important. Learn this fact.

Answer 10

Now, given that. Suppose it were true that f(x) had no local min or max on the real line.

That would mean f'(x) is nowhere zero.

So to find out if it is indeed the case that f(x) has no max or min, you need to see if f'(x) is ever zero.

Answer 11

found the first derivative test...

Answer 12

What then is f'(x) and is it ever zero?

Answer 13

take a plug a value into the derivative of a function and then see whether each side is + or - and if both side of c are the same side then point is neither

Answer 14

You need to go back to your text book and class notes, and spend a good couple of hours, reading them, taking new notes, verifying results.

Right now you don't have a very good understanding of what's going on here.

Do that and then all of these questions you're asking will be easier.

Answer 15

that is what i am doing