1). it is increasing at [-2,0]u[0,2] because the output is positive, above the x-axis. it is decreasing at (-∞,-2]u[2,∞) because the output is negative, below the x-axis.

2). there is a local minimum at x=0, and local maximum at x=-1.25, 1.25.

3). you cant tell with this graph because it is the graph of f '(x), it doesnt show the f(x).

4). the power function of f(x) is 5. it is 5 because the graph of the derivative has 4 slopes. by that i mean it changes the sign of the slope 4 times. so to get the derivative you subtract 1 off the power function and to find the f(x) you just add 1 to the f '(x).

Mindsets

1). i think that i am more a part of the growth mindset when it comes to intelligence. i see a lot of things as challenges and that makes me want to work harder. also im persistant,and i see criticism as a way to find out what i did wrong and how i can make it right.

2). this mindset has helped me in math because i dont let setbacks get to me. also i learn from criticsim, that is what gets me to understand what we learn in class. it also makes me understand i better.

3). knowing that my brain is a muscle and that i can train it makes me feel in control. it makes me feel like i control what goes in to my brain. also puts me at ease to know that i can train my brain.

4). i see it as a way to make learning a bit easier. i feel like i can train my brain just as if i were to train a dog but in sort of a good way. this info just puts me at ease.

whats the difference?

1). the difference between finding the limit of x=c and actually plugging in the number x=c has to do with what you're trying to figure out. when you're finding the limit you are actually looking for numbers as you get closer to x=c.in other words your trying to get somewhat of a picture of how the function is going to look like. when you're plugging in x=c you are finding actual points and therefore you will be able to graph the function. this will be the actual way the function looks like.
also the two are the same when the limit of f(x) as x->c- and f(x)
as x->c+ are equal to f(x) as x->c.

2).the major similarity between finding the derivitive and the slope of a line is that you're finding the slpoe of a line. the difference is that for the derivative you're trying to find the slope of a specific line, a tangent line.

Colleges

1). Bussiness: this is something that almost anybody could get in to. it is a practical choice because it is used in almost every job. with this major people will not only have the skills to start their own business but also have the skills need to excel in other jobs.

Engineering: a career inengineering is computer engineering and that is a very interesting career. there people have to work with sofeware and its design. people in these kinds of jobs focus on how computers work and on there function. later they could work on robotics and on motors, communicatons, and sensors.

Culinary Arts: this is a major that is really interesting. in this career people learn how to cook food and get titled as chefs or cooks. this may not look that hard but for this people must know about the science of food and nutrition. also they are skilled in creating food that is good, nutritious and eye pleasing.

2).DeVry Universiry: this university has one of the best business programs. it has a 94% rate of graduates that graduate form a business major and go on to get business related careers. if people do good they could end up getting their degrees in as little as 3 years. but beside business, DeVry has 90% of their graduates in active jobs, which means that they dont struggle with getting jobs.

Ohio State University: this university offers more than 160 academic programs acount from zoology. it has a great engineering program, one of te top in the country. also it has alot of undergraduates which are involved in programs that take them around the world. also it has a great football team, just saying.

Kendall College: it is a culinary arts school that teaches the art of crafting great foods. 97% of their graduates find jobs within 6 months after graduating. plus the campus has everything needed for people to get a great learning experience. they top quality kitchens and also have great cafeteria food. so Kendall is a great if you are into cooking or want to learn to cook.

Hints and Tips

1). Transformations:

transformation are pretty easy to know. for example, lets say you were given this equation, f(x)=-(x-8)+5. first of all whatever is in the parenthesis determines whether th function shifts to the left or right. if you are adding then it goes to the left if you are subtracting then it shifts to the right. next whatever you are adding or subtracting to the parenthesis determines whether it goes up or down. adding means it goes up, subtracting means it goes down. if there is a negative sign in front of the the parenthesis that determines if the function goes up or down. a negative sign means it goes down, if there isn't any then it goes up.

2). Trigonometry:

when it comes down to the unit circle, i get it. i had to memorize the unit circle for my last math class so its kinda stuck in my head. its easy to remember the radiants, also its easy to determine whether they are negative or positive when you know the quadrants. all i have to know is that pi/6=(root of 3/2, 1/2), pi/4=(root 2/2, root 2/2), pi/3=(1/2, root of 3/2), and pi/2=(0,1). once i get those down everything else is just a mirored image of these radiants.

3). What Confuses Me???

things that still confuse me are sin, cos, tan, cot, csc, and sec. i get mixed up with the equations. also i still dont know their domain and range but i just have to try and memorize them.

Inverses and Logs

from what i understand about inverses is that they are the complete opposites of each other. for example, the inverse of (f) is (f^-1). if you are squaring something then in the inverse you would have to square root it. or another example would be if you are multiplying by, lets say, 3 then in the inverse you would have to divide by 3 instead. thats what i understand about inverses.

first of all the default base of a log is always 10. usually an example of a log would look like this, log100=x. this would turn out to look more like this, 100=10^x. now the answer is x=2 because 10 squared is equal to 100. this is pretty much what i get from logs. also if the base and the little number right after the word log are the same then they cancel out.

questions:

• are ln and log the same things?

EVEN and ODD Functions

Even: the equation to find out if a function is even is f(-x)=f(x). this means that the function will be symmetrical to the y-axis. in other words, when the function is graphed, quadrant 1 and quadrant 2 will be a reflection of each other. so an even function looks the same as it is reflected over the y-axis.

ODD: the equation to find out if a function is odd is f(-x)=-f(x). this function will be symmetrical to the origin. in other words, this function will go through the origin and also it will remain the same as it is reflected over the x-axis and y-axis. it is taking the graph in quadrant 1 and reflecting it on both the x and y-axis.