Question

http://www.wolframalpha.com/input/?i=y%3D%282cos+3x%29-1+
What points does the graph cross the x-axis?

Answer 1

it crosses the x-axis when y=0

Answer 2

so solve\[0=2\cos(3x)-1\]for x

Answer 3

http://www.wolframalpha.com/input/?i=0%3D2cos%283x%29-1 ?

Answer 4

so yeah, the answer is on there
but why don't you try to do this without wolfram since you obviously aren't learning much from that site?

Answer 5

Well I am, it's just faster :/ Thank you though

Answer 6

Oh wait, can you please confirm? The absolute max is 1 and the absolute min is -3?

Answer 7

@TuringTest

Answer 8

Hello? You there?

Answer 9

sorry I was afk

Answer 10

max/min is when the derivative=0
so what is the derivative of this function?

Answer 11

I'm not sure :/

Answer 12

are you in calculus yet?

Answer 13

Nope

Answer 14

well what are the max and min values that y can be? (look at the graph, what is the highest/lowest it goes?)

Answer 15

oh you have it already, but those are not absolute max's or mins because they reoccur

Answer 16

absolute max/mins are like the highlander: "there can be only one"
hence there is no absolute max or min on your graph, just a infinitely many relative ones

Answer 17

http://www.wolframalpha.com/input/?i=y%3D%282cos+3x%29-1+ So for this graph there are NO absolute maximum or minimum?

Answer 18

are you given an interval, or are you talking about the whole graph?

Answer 19

The whole graph

Answer 20

I want to say then the answer is "no" because of what I said earlier, but now I am starting to doubt myself and am looking for a formal definition of absolute max and min values
one sec plz

Answer 21

Oh o.k. No problem, thank you so much

Answer 22

okay I was quite wrong, good thing I double-checked:
"A function has a global (or absolute) maximum point at x∗ if f(x∗) ≥ f(x) for all x. Similarly, a function has a global (or absolute) minimum point at x∗ if f(x∗) ≤ f(x) for all x."
so because we have \(\le,\ge\) and not \(<,>\)
so there can be more than one, and they are what you said they are :)

Answer 23

Oh cool! Thanks so much for double checking because I wasn't even for sure myself. I appreciate your help, time, and patience :)

Answer 24

thanks for forcing me to learn something
if you hadn't pressed me to be sure I might have kept telling people the wrong thing :P