F(x) from F'(x)

1. f(x) is increasing between [-2, about 1.3)U[0, about 1.3). I could tell this is the answer from the graph shown because wenever f'(x) has a positive output is where f(x) is positive.

2. local min at x= -2
local max at x= 2
Extrema can only occur when f'(x) is equal to 0 or is undefined, which is characterized by those two points. At x= -2 the sign changes from negative to positive therfore it being a local min. At x=2 the sign changes from positive to negative therefore being a local max.

3. The function f(x) is concave up at (-1,1) and convave down from (- infinity, -1)U(1, infinity). A function is concave up whenever f"(x)>0 and concave down when f"(x)<0. you can tell Weather its concave down when you see the graph of f'(x) is decreasing and concave up when the graph of f'(x) is increasing.

4.The graph of f'(x) would defenitly be a polynomial equation to the 4th power, now taking in consideration that the graph is the derivative of the origional graph f(x) must be a polynomial to the 5th power. p.s I looked at the notes ms.hwang gave us on how to tell how a polynomial equation would look if its higher than an equation to the 3rd power.

Fixed vs. Growth Mindset

1. When it comes to "intelligence" i think i have a growth mindset. I see "intelligence" as something everyone can be at a high level if everyone has dedication to what they do not caring of what everyone thinks of you. The reading tells me that i am because I personlay like challenges, i think they help you understand a certain subject more. I really don't mind of others critisism, unless its of my work i will pay attention an learn from my mistakes.
2. This mindset has helped me in math because it has allowed me to attend the class I am attending right now, calculus. If it was'nt for this mindset i would have stoped at what was requiered to graduate High School, but i decided to out do myself. This mindset has hurt me because sometimes for trying to outdue myself i tend to get low grades in class and grades in tests that i have never gotten in math. :/
3. Well i personally already knew that the brain is just like any muscle that can eventually be trained. There is no stupid person, its their efforts that ar stupid not the person.
4. This will affect my future because now i know that any challlenge in life i take to see what exactly i am capable of.