Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

Given: enter image description here

Why is -2 non-inclusive?

share|cite|improve this question
up vote -2 down vote accepted

The derivative of the function (the slope) is 0 at x = -2.

The definition of an increasing function requires that the slope be strictly positive. :)

share|cite|improve this answer
I presume you mean strictly increasing and are talking about continuously differentiable functions. Then if the slope is positive, it's true that $f$ is strictly increasing, but not the converse; consider $f(x)=x^3$. – Michael Hoppe Feb 28 '14 at 13:32
This is not correct. – Mark McClure Feb 28 '14 at 14:16
@MarkMcClure Do you mind to explain my error? – Michael Hoppe Feb 28 '14 at 14:25
@MichaelHoppe I mean this answer is incorrect - yours is the correct one! I even upvoted it! – Mark McClure Feb 28 '14 at 14:35
@MarkMcClure thanks for clarification. – Michael Hoppe Feb 28 '14 at 14:39

The function is strictly increasing on any interval $J\subset(-\infty,-2]$, so the suggested answer is true since $(-\infty,-2)\subset(-\infty,-2]$.

share|cite|improve this answer
This is correct. – Mark McClure Feb 28 '14 at 14:15

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.