1.) Where is the function, f(x), increasing? Where is it decreasing? How can you tell from this graph? Explain.
on this graph the F(x) is increasing between (-2, 0) U (0, 2) tha is because on this interval is the only time that f'(x) produces positive outputs and not outputs that are equal zero or negative numbers.

2.)Where is there an extrema?
Well on this graph it seems that there are three extrema points. One piont is at F'(0) that is because at that pointis when f'(x) is equal to zero alos there is a change of signs there from being negative to positive so this would be a local minimun. the other two extremas would be when f'(x) is equal to both + and - 1. 25 at these points there are both local maximums.

Where is the function, f(x), concave up? Where is it concave down? How can you tell from this graph?
on this graph it concaves up between (-∞, -1.25) U (0, 1.25) because in this interval is the only time the derivative of this graph would be positive and it also be f''(x) which would make it true.
between (-1.25, 0)U(1.25, ∞) is where is concaves down. on that interval the f'(x) makes anegative slope so then on the double prime graph there would be a negative value on the double prime

Sketch the graph f(x) on a sheet of paper. Which power function could it be? Explain your reasoning.
well it seems that the power graph is x to the fifth by the way the graphs are turning up. Because the f''(x) looks like a graph of x to the thrid power so then the original graph would have the parent fuction is x to the fifth.

mindsets

1.) the mindset that mostly would suit me would be a bit of both actually. The growth mindset would suit me at times because at times I just want to learn more and comprehend more things while I am learning. Like for instance on tests when we get it back I try to learn my mistakes from it and try to never make those type of mistakes from it so that would make me a growth mindset at times. But at the beginning I sort of felt that I was also a fixed mindset. I fell that I am like that at times when it comes to my homework because there are problems that if they seem really difficult I just give up and don't try at all and avoid it and move on. so in a way take the blogs for example I try to avoid them as much as possible so that would make me a fixed mindset but in a way I want to change that, but so far it is hard to change old habits. but overall I think that I have more of a fixed mindset than a growth one.

2.) well having a fixed mindset has really hurt me because well I don't try as hard which shows up in my grade and well i give up half way. It is mot something I am proud of but at times I think "why bother" so that takes away my motivation at times and don't even get half way at times. but later on the growth mindset kicks in and i try to finish at times. I guess in tests it has helped me because I try to not to leave any answer blank also I accept what I did wrong and try not to repeat the step but since I have more of a fixed mindset it has really hurt me more than benefit me.

3.) The way I reacted was a bit surprised because no one has ever said that about the brain and well that sort of surprised me. Like there are lessons to help out the subject that you are trying to learn but never have I heard lessons to excercise your brain.

4.) By reading this I have learned that change is possible to cahnge the way I think and if I do continue Calculus I hope that it will change along the way because it seems that it is a lot more beneficial to have a growth mindset than a fixed one. And next time I get stuck on a problem I'll remind myself that I have to get that i can always finish even if my mind tells me that it is relly difficult.