DOE functions for R (version #4)
The file DOE_functions_v4.R contains a collection of R functions that simplify some of the
most common analyses in DOE, and especially in RSM:
The symbols <> are used to express the contents of an R object.For e
First comments on some things that appeared during the class.
1) Can you have legends on plot? Yes you can, and I added an example in Spectra.r that can
be found in the address given below. I also added an example of using mathematical
annotation in the l
The files that I created today (15.4.2016) can now be found in
Your fourth assignment is to repeat the analyses we did today with the iris data using the wines
data. You may imitate the analyses
The files that I created today (8.4.2016) can now be found in
Your third assignment is to repeat the modelling of Nt as a function of the NIR spectra using some
spectral pretreatment. Use the pr
9.3 Rates of Change and Derivatives
For linear functions, we have seen that the slope, m, of the line measures the average rate of change of the function
and can be found from any to points on the line via m =
For a function tha
10.1 Relative Maxima and Minima: Curve Sketching
Recall: The graph of a quadratic function, f (x) = ax2 + bx + c with a = 0, is a parabola. The graph has a turning
point located at its vertex, which is found via the vertex formula:
10.3 Optimization in Business and Economics
Denition: Absolute Extrema
The value f (a) is the absolute maximum of f if
for all x in the domain of f (or over
the interval of interest).
The value f (a) is the absolute minimum of f if
10.2 Concavity; Points of Inection
A curve is said to be concave up on an interval (a, b) if at each point on the interval the curve is
its tangent at the point. If the curve is
all its tangents on a given interval, then i
9.5 The Product and Quotient Rules
In the last section we discussed numerous dierentiation rules. We stated that unlike constant multiples, addition,
and subtraction, dierentiation does not play nice with multiplication and division. Again, c
9.2 Continuous Functions; Limits at Innity
In the previous section, we found that if f (x) is a polynomial function, then lim f (x) = f (c) for all values of c. Any
function for which this special property holds is called a continuous func
12.2 The Power Rule
Using the only integration technique we have studied (the Powers of x Rule), can we evaluate the following integral?
(4x2 7)3 8x dx
If y = f (x) is a dierentiable function with dy/dx = f (x), then the
In various applications we have seen the importance of the slope of a line as a rate of change. We were able to discuss
the slope of linear functions because their slope is constant; that is, the steepness of the line did not depen
9.6 The Chain Rule and the Power Rule
Thus far we have only investigated how to take a derivative of fairly simple functions like those below.
f (x) =
g(x) = 4x5 x3 3x2 + 1
4x3 + 2x2 x 3
But what if we wanted to take the
11.1 Derivatives of Logarithmic Functions
Logarithms are concerned with powers (or exponents)!
Recall: Logarithm Basics
The logarithm denition: by = x y = logb x
The logarithmic function y = logb x has base b and domain (0, ).
The natural loga
9.9 Applications: Marginals and Derivatives
Revenue and Marginal Revenue
If the demand function for a product is p = f (x) where p denotes the price per unit, then the total revenue
from the sale of x units is
If R = R(x) is the total rev
12.1 Indenite Integrals
So far, we have studied procedures and applications of nding derivatives of a given function. We now turn our
attention to the reverse direction. That is, given a derivative f (x), how do we nd f (x)? This process is c
11.2 Derivatives of Exponential Functions
Recall: Exponential Functions
The function y = bx is an exponential function with base b, where b > 0 and b = 1.
The natural exponential function y = ex has base e 2.71828.
Derivative of y = ex
If y = e
9.4 Derivative Formulas
As one can imagine, nding the derivative of a function via the denition is going to become extremely tiresome.
Luckily, we do not always need to resort to such tedious endeavors! Consider the following derivatives:
9.8 Higher-Order Derivatives
Because the derivative of a function is itself another function, one might ask how is the derivative changing? To
answer that question, one would just take a derivative of the derivative since derivatives tell us
12.3 Integrals Involving Exponential and Logarithmic Functions
If u is a dierentiable function of x, then
eu u dx =
ex dx =
Example 1: Evaluate each indenite integral.
Your Turn 1: Evaluate each ind
12/6/16, 3:40 PM
Board Query 1
You have answered 1 out of 10
questions. Select your next
question or close the Quiz
when you are done.
2006 Capsim Management Simulations, Inc.
Investing $2,000,000 in TQM's Channel Support Syst
Ashley Gazewood Math 1600 MW 2:30
Problem Statement: How to find the area of various geometric figures, using the same formula Area = Base times Height. Describing how these formulas were developed and what do they mean? Activity Log: For thi