Trigonometry and Statistics) A. Functions 1. Demonstrate knowledge and skill related to functions in general 1.1 Define a function 1.2 Differentiate a function from a mere relation * real life relationships * set of ordered pairs * graph of a given set of ordered pairs * vertical line test * given equation 1.3 Illustrate the meaning of the functional notation f(x) 1.4 Determine the value of f(x) given a value for x B. Linear Functions 1. Demonstrate knowledge and
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n calculus‚ Rolle’s theorem essentially states that a differentiable function which attains equal values at two distinct points must have a point somewhere between them where the first derivative (the slope of the tangent line to the graph of the function) is zero. ------------------------------------------------- Standard version of the theorem [edit] If a real-valued function f is continuous on a closed interval [a‚ b]‚ differentiable on the open interval (a‚ b)‚ and f(a) = f(b)‚ then there
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Consumer Research Methods Market research is often needed to ensure that we produce what customers really want and not what we think they want. Primary vs. secondary research methods. There are two main approaches to marketing. Secondary research involves using information that others have already put together. For example‚ if you are thinking about starting a business making clothes for tall people‚ you don’t need to question people about how tall they are to find out how many tall people
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.........3 RECOMMENDED 2-UNIT OPTIONS......................................................4 MATHEMATICAL MODELLING............................................................4 UNIT 1: ALGEBRA‚ GEOMETRY AND CALCULUS MODULE 1 : BASIC ALGEBRA AND FUNCTIONS...........................7 MODULE 2 : TRIGONOMETRY AND PLANE GEOMETRY .............18 MODULE 3 : CALCULUS I ..............................................................23 UNIT 2: ANALYSIS‚ MATRICES AND COMPLEX NUMBERS MODULE 1 : CALCULUS II .
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Structured program list. First unit: Sets. In this unit the fundamental concepts of the theory of sets is addressed to provide the tools and the language of operation for subsequent units. Second unit: numbering systems. In this unit‚ we address numbering systems of different cultures until the one’s used current day‚ highlighting the importance of ten based numbering system (decimal)‚ which will be developed in depth by tackling its properties through the next unit. Unit Three: The field
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looking for at Store A. In Store A‚ the bracelet without charms costs $85 and each charm costs $15. A. Use function notation that models the total price of the bracelet and how that price is based on the number of charms. Explain the reasoning behind your equation. 15W=85 IN ORDER TO FIND THE NUMBER OF CHARMS YOU NEED YOU HAVE TO DIVIDE. B. What would be a reasonable domain for this function based on this scenario? Explain why this is a proper domain. C. If Marco and his sisters have saved $250
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to evaluate logs‚ trigonometric functions‚ and exponents? This ability is due in large part to the Taylor series‚ which has allowed mathematicians (and calculators) to approximate functions‚such as those given above‚ with polynomials. These polynomials‚ called Taylor Polynomials‚ are easy for a calculator manipulate because the calculator uses only the four basic arithmetic operators. So how do mathematicians take a function and turn it into a polynomial function? Lets find out. First‚ lets assume
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__ The total amount of revenue made by the Miramar Resort Hotel is given by the function ‚ ‚ where x is the amount of money the hotel spends on advertising its services‚ and where both revenue and x are measured in thousands. 1. Using Wolfram Alpha‚ graph the revenue function over the given domain and paste the graph here. 2. Compute the marginal revenue function and copy and paste a graph of this function on the domain here. Then use Wolfram Alpha to determine where revenue is increasing
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coordinates of all relative extreme points of[pic]. |A)[pic] |B) [pic] |C) [pic] |D) [pic] |E) [pic] | [pic] First find the derivative of the function[pic]‚ f ’(x): |[pic] |= |[pic] |apply power rule of differentiation | | |= |[pic] |simplify
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construct the polynomial function‚ f(x)‚ that will be the path of your roller coaster. Show all of your work. Answer: To create the polynomial function‚ we would need to find the three roots to create factors. The roots would be the x-coordinates‚ 6‚ -2‚ and -7 so the factors are x-6‚ x+2 and x+7. Now multiple x-6 and x+2 to get x^2-4x-12. Take that answer and multiply it by the third factor‚x+7 and it would result with x^3+x^2-28x-12x-84. Combine like terms and the polynomial function is f(x) = x^3+x^2-40x-84
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