Transcription of SECTION 1.10: DIFFERENCE QUOTIENTS - kkuniyuk.com
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SECTION 1.10: DIFFERENCE QUOTIENTS - kkuniyuk.com
( SECTION : DIFFERENCE QUOTIENTS ) SECTION : DIFFERENCE QUOTIENTS LEARNING OBJECTIVES Define average rate of change (and average velocity) algebraically and graphically. Be able to identify, construct, and evaluate (and simplify) various forms of DIFFERENCE QUOTIENTS . PART A: DISCUSSION This SECTION will revisit SECTION on slopes of lines, SECTION on function evaluations, and SECTION on graphs. A DIFFERENCE quotient is used to find the slope of a secant line to a graph or to find an average rate of change (perhaps an average velocity). DIFFERENCE QUOTIENTS will form the basis for derivatives, tangent lines, and instantaneous rates of change in SECTION PART B: SECANT LINES and AVERAGE RATE OF CHANGE The secant line to the graph of a function f on the interval a,b , where a<b, is the line that passes through the points a,fa()() and b,fb()().
(Section 1.10: Difference Quotients) 1.10.3 The average velocity is 50 mph on 0, 2 in the three scenarios below. It is the slope of the orange secant line.
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CONTINUITY AND DIFFERENTIABILITY, MECHANICAL ENGINEERING UNIT 1: ENGINEERING, MECHANICAL ENGINEERING UNIT 1: ENGINEERING MATHEMATICS, Differentiability, CIVIL ENGINEERING UNIT 1: ENGINEERING MATHEMATICS, Syllabus for Mechanical Engineering ME, Mathematics mathematics, Practice, MATHEMATICAL SCIENCES, MATHEMATICS CLASSES XI