How to Prove that a Function is Always Increasing or Decreasing

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In this video, I will teach you how you can show that a function is always increasing or decreasing. To do this I will take you through the theory and show you two fully worked examples that explain how to prove whether a function is increasing or decreasing using the first derivative test.
  1. The Complete Guide to Everything
  2. how to prove a function is increasing
  3. how to prove a function is decreasing
  4. how to prove a function is always increasing
  5. proof a function is increasing
  6. increasing and decreasing functions
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Amazing video, you've helped me understand so well! Well earnt sub :) Take care

teatime
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I have a book that says that for the function y to be always increasing the derivative (y') has to greater than or equal to zero (that I get) and then for the derivative of the function (y') to be greater than or equal to zero the Discriminant D of the derivative must be less than or equal to zero and I don't understand why the discriminant has to be negative or zero? I am missing the relationship. the problem in the book is as follows : find the values of a for which y = x^3 + ax^2 +3x +1 is always increasing. So I can solve it if I make the D less than equal to zero and get -3 <= a <= 3, but I don't know why, why am I to set the D in this way. Thanks for your help.

noagenda
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nice1

may i ask which app are you using in this video?
is this power point?

Eran-wp