Business Calculus 1. Where calculus did came from?
-calculus was created by Isaac newton (Bristish scientist) and Gottfried Leibniz (German Mathematician) in 17th Century
- Isaac Newton discovered inverse relationship between the derivative (slope of a curve) and the integral (area beneath it. Applications for calculus were geometrical and related to physical world.
- Gottfried Leibniz – calculus was more about analysis of change in graphs.
2. Who are the father of calculus?
Isaac Newton and Gottfried Leibnitz 2. Why study Calculus? * Calculus is the study of how things change and provides framework for modeling systems in which there is change and a way to deduce the predictions of such models; Calculus provides a way for us to construct relatively simple quantitative models of change and to deduce their consequence. By studying this, you can learn how to control the system to do make it do what you want it to do.

CHAPTER 1: FUNCTIONS AND LIMITS
FUNCTIONS
* A bunch of ordered pairs of things with property that the first members of the pairs are all different from one another.
Ex [ {1,1,}, {2,1}, {3,2} ]
Arguments – first number of the pair
Domain – whole set
Values – Second number of the pair
Range – set of values
Classification of functions 1. Linear Functions – “steepness of the line” w/c can go uphill or downhill. y = mx + b

2. Quadratic Functions – it has a degree and forms a parabolic path. The highest (or lowest point) of the parabola is called the vertex. At has a form of
(standard form of quadratic equation)
F(x) = Ax2 + Bx + C where A, B,C are constant.

Vertex form of Quadratic
F(x) = a (x-h)2 + K
Quadratic Formula

3. Polynomial Functions – a quadratic, a cubic, a quartic and so on involving only non-negative integer powers of x. 4. Rational Function – quotient of two polynomials
P(2) and Q (2)

Sometimes called rational polynomial function. If P and Q are polynomials in multiple variables, their quotient is called a (multivariate) rational function. The term “rational polynomial” is sometimes used as a synonym for rational function.