Mean Value Theorem

The mean Value Theorem states that for a function to have a tangent line parallel a chord AB then it must be continuous at the interval [a,b],where the chord is located.

Algebraically speaking it means this: f'(c)= f(b)-f(a)/(b-a)

Graphically it looks like this:

Instances when the mean value theorem fails to work are when the graph is either not continuous or not differentiable on the interval that the chord is located
The graph above is not differentiable between the intervals that the chord is located therefore it has no tangent line parallel to ab.

Mindset Questions

I'm more of a fixed mindset person than a growth one. A lot of the definitions of a fixed mindset person describe me, but not all the time and not completely. It's impossible for someone to adhere to such a limited philosophy;impossible to view the world with such a narrow perspective.I make a lot of mistakes in life and I have my regrets. I've avoided challanges,fallen against greater obstacles, and felt defeated,but I've had my moments of triumph.Those rare moments that seem to make everything right,until I screw things up again. I've screwed up a alot, but that doesn't mean I don't try to change. It doesn't mean I'm always going to be this way and that I'm always going to think the same.

This mindset has hurt me bad, real bad. It has overwhelmed me and just buried me. It has caused me a hell of a lot problems. I've fallen behind and almost completely given up. And what remains is just a seemingly unwinnable situation. Seemingly because it can be won, and it may. It'll just take a clear head and some patience. Two qualities I don't have, or ever had.

My reaction was not so much shock or anything like that. My reaction was more like quiet indifference. It wasn't anything new. I've heard it before,I don't recall from where, but I've heard it. I've know about it for a while. It's just that I haven't put in practice because of laziness or another such and such reason.

Well, I really need to change. I have to stop procrastinating learn to be more responsible. It's a usefull piece of information, but hard to put to good use without proper motivation and will-power. I don't know how its going to affect me in the future, hopefully good.