10/16/06 Class Notes
Yes, I know, this is late but I had problems with formatting and the synthetic division thing. So anyways, here are the 10/16/06 class notes:
A. Took a quiz on limits
B. Went over the 3-3 homework
-There is no derivative at a cusp because the tangent line is straight up which has no slope
C. Exploration 3-4 – Derivative of a power function
Derivative of x^5 at x=c is 
Using synthetic division, this can be simplified to x^4+cx^3+c^2x^2+c^3x+c^4. As x approaches c, we can replace x with c, resulting in c^4+ c^4+ c^4+ c^4+ c^4, or 5c^4. With any power function of nth degree, the derivative is nx^(n-1).
-If there is a constant, k, multiplied by the power function, the derivative is knx^(n-1)
-The derivative of a polynomial, a sum of power functions, is the sum of the derivatives of each term of the polynomial
-For example, with the polynomial 3x^3+4x^2, the derivative is 3(3x^2)+4(2x), or 9x^2+8x
-ƒ’(x)=, y’=, and 
all are ways to show the derivative of a function.
