I have a question about notation. Just let me write it out.
Stacey Warren - Expert brainly.com
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\[3x^2 >= 0\] \[\forall x \] (three dots like a triangle upside down) x^2 is always positive.
Sorry for the line spacing, it should all be on one line.
Would this read: "3x^2 is more than or equal to 0 for all x because x^2 is more than or equal to zero" ?
Thank you, but it was the latter part I wasn't sure about.
For all x
And the triangle ( http://en.wikipedia.org/wiki/Because_sign )
Thank you! Is that correct notation? I mean would it "grammaticly" correct?
are you trying to do set builder notation?
Are you trying to determine the solution of that inequality?
The original problem was.
Prove that x^3 - ax is increasing for all x if a < 0
But I wanted to use proper notation.
Is this calculus, where you are proving intervals that are increasing and decreasing?
Yes this calculus, but the calculus wasn't the problem, it was just the notation
Usually when you are asked to prove an increasing or decreasing interval.
Step 1: You take the derivative of the given function
Step 2: You take that equation and set it equal to zero and solve
the solutions that are positive represent increasing
the solutions that are negative represent decreasing
I am not sure you were on the correct track
Nevermind what you solution is, the professor would have realized that you were not doing the problem correctly.
Stating the wrong solution correctly does not make the solution correct.
In mathematics we look for the correct process, correct solutions and correct
mathematical notation ie set builder notation