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About Brian Davidson
Expertise
I can answer questions ranging from Pre-Algebra through AP Calculus BC (first year college calculus), as well as some questions in Discreet Mathematics (probability, matrix theory, graph theory, and combinatorics).
Experience
From my earliest years as a math student, I have dedicated myself to learning the concepts and discipline of mathematics.
In addition to a rigorous mathematics course sequence throughout junior high and then high school, I have served for four years on my school's math team and won several first place awards in both state and national competitions. I earned a perfect score on the AP Calculus BC exam, and (in addition) have done in-depth course work in discrete mathematics and differential calculus. Of course, I more commonly find myself offering aid in less advanced forms of math, which is why "Math for Kids" is perfect for me, also given my education credentials and previous experience.
Education/Credentials
Although I am just a college student, my educational experiences are broad. I have served as a certified student tutor for mathematics and physics both inside and outside of high school (2005 to 2009), served as a student leader by helping teach an integrated science/math class at my high school, where I was able to develop my teaching style through lessons and group interaction. Although I have much to learn before beginning to teach professionally (as I plan to do), I am proud to have helped over 80 students achieve success in mathematics over a four year period, all while expanding my own knowledge and appreciation for the discipline. And although I have studied many advanced forms of mathematics, some of my most successful students came to me for help with pre-algebra, algebra, or elementary geometry.
Awards and Honors
Outstanding Student Teacher Award (2009), Senior Student Tutor/Seminar Lecturer (2008), 3 First-place mathematical olympiad finishes, 4-second place.
Past/Present Clients
I have tutored between a 80 and 90 fellow students (both same age and younger) during high school before my graduation, although for privacy reasons, I'd rather not give specific names in such an online context. If more information is needed, please feel free to contact me through private email at bldavidson1990@hotmail.com
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You are here: Experts > Science > Math for Kids > Math for Kids > ap calculus ab
Expert: Brian Davidson - 10/27/2009
Question
My Problems (set 1):
22. In Exercise 22, find the formula for the slope of the graph. Use the formula to find the slope at the two points.
This is what is given --- g(x) =(x³) (a) (1, 1) (b) (-2, -8)
24. In Exercise 24, find the formula for the slope of the graph. Use the formula to find the slope at the two points.
This is what is given --- g(x)=radical(x-1) (a) 5,2) (b) (10,3)
[DN1] Find the slope of y=3x² at the point (-2, 12).
Answer
Asad,
22. The function is g(x) x^3. To find the slope of the graph, we must find the formula for the derivative of the function (since this is 1st semester calculus, I'm assuming you are familiar with the definition of a derivative--it's just the slope). The derivative of (x^3) is 3x^2 (in general, the derivative of x^a is ax^(a-1). So we know that at WHATEVER point we choose, the slope at that point (for the function given) will be found by plugging in "x" into 3x^2 (the derivative).
So for (1,1), we have : slope = 3(1)^2 =3 For (-2,8), we have slope = 3(-2)^2 = 12.
24. We know that g(x) = rad(x-1). This is the same as saying g(x)= (x-1)^(1/2) (by the definition of square root)). So we can use the same formula as above to find the derivative.... The derivative will be 1/2*(x-1)^(-1/2). Remember, the derivative of x^a is ax^(a-1). So plugging in "5" for x and "10" for x (into 1/2*(x-1)^(-1/2) will give the answer... I'll leave it to you to do that step.
When considering y=3x^2, we again take the derivative. The derivative is equal to (3)(2)(x^1) which is 6x. So the slope will simply be 6(-2) =-12
I hope that helps..Feel free to follow up, as always!
-Brian
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