Rule 1: Derivative of a Constant
The derivative of a constant function is equal to zero
- The graph of a constant function is a line parallel to the x axis
Rule 2: The Power Rule
If n is any real number, then (xn ) n
The derivative of ln x
ln| x| (x 0)
To derive the rule, suppose x>0 and write f(x)=ln x in the equivalent form x=ef(x)
Differentiating both sides of the equation with respect to x, we find using the chain
- We assume that
to simplify the derivation of the
- The result is valid without this restriction
- Begin by dividing the interval [a,b] into subintervals of equal length
- By means of the (n+1) points x-0= a
Antiderivatives and Rules of Integration
A function f is an antiderivative of f on an interval I if F(x) =f(x) for all x in I
An antiderivative of function f is a function F whose derivative is f.
For example, F(x)=x2 is antiderivative of f(x)
Function: A rule that assigns to each element in a set A one and only one element in a set B.
The set A is called the domain of the function.
Y=f(x) as x takes on all possible values in its domain, is called the range.
- Domain is a se
Chapter 4.2 Intervals of Concavity
First Derivative f: Is the slope the first derivative tells us how whether a
function is increasing or decreasing, and by how much it is increasing or
decreasing. This information is reflected in the graph of a function
Open Interval: The set of all real numbers that lie strictly between two fixed
numbers a and b is called an open interval (a,b). It consists of all real numbers x that
satisfy the inequalities a<x<b. and it is called open because neith
MATH 1P98: Practical Statistics (Spring 2017)
due Thursday, May 18th (in class)
For our assignments we will be using two different computer programs for each assignment.
Excel is available on your e-mail as part of the Office 365 package. The
MATH 1P98: Practical Statistics
Instructor: Andrew Skelton
e-mail: [email protected]
All announcements, assignments, solutions, lecture notes and grades will be posted on the
course website on Isaak. https:/lms.brocku.ca/port
1p92 Sample final exam questions
1. The diagram below shows the AE line for the economy.
a) Label the autonomous expenditure A in the diagram.
b) Label the equilibrium level of GDP B on the diagram.
c) Government spending now increase
8.1-Functions of Several Variables
Functions of Two Variables
A real-valued function of two variables consists of
1. A set A of ordered pairs of real numbers (x,y) called the domain of the
2. A rule that associates with each ordered pa