# Approaching the tangent line define the derivative as

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Unformatted text preview: nt to a curve at any given point Identify the notation developed by both Newton and Leibnitz Practice sketching tangent lines and estimating slope Define “derivative” as the limit as h approaches 0 of (f(x+h) – f(x))/h and interpret as the slope of the secant line approaching the tangent line Define the derivative as a function Sketch the derivative as a new function with the coordinates (x,m) in which m is the slope at any given point x Sketch the derivative of a function free hand using critical points such as “peaks” Recall various discontinuities of functions at which the function is not differentiable: cusps, corners, jumps, asymptotes and holes NJ CCCS Strands & Indicators 4.1 4.2 4.3 4.5 A,B,C C A,B,C,D A,B,C,D,E,F 4.1 4.2 4.3 4.5 A,B,C C A,B,C,D A,B,C,D,E,F Suggested Timeframe (in blocks) 2 2 Course Objective(s) Present all algebraic properties of the derivative in relationship to the original function Student Objectives • • • • Examine the derivative as “velocity” • • • Apply derivative computation to trigonometric, exponential, logarithmic and miscellaneous functions • • • • Review the “limit” definition of the derivative Use the “power rule” to find the derivative of a function: f’(x) = nx n-1 Apply the Chain Rule when finding the derivative of a composition of functions Apply Product and Quotient Rules to finding more complex derivatives Identify the first derivative as “instantaneous velocity” and its connection to “speed” Identify the second derivative as acceleration Distinguish between instantaneous & average velocity Practice derivative rules with trigonometric functions Review and apply properties of ex and ln x Identify the derivatives of absolute value, greatest integer and piecewise functions Apply Chain, Product and Quotient Rules NJ CCCS Strands & Indicators Suggested Timeframe (in blocks) 6 4.1 4.2 4.3 4.5 A,B,C C A,B,C,D A,B,C,D,E,F 4.1 4.2 4.3 4.5 A,B,C C A,B,C,D A,B,C,D,E,F 1 4.1 4.2 4.3 4.5 A,B,C C A,B,C,D A,B,C,D,E,F 5 Course Objective(s) Demonstrate the method of Implicit Differentiation Student Objectives • Apply implicit procedures for differentiating equations of circles, hyperbolas and ellipses NJ CCCS 4.1 4.2 4.3 4.5 Strands & Indicators A,B,C C A,B,C,D A,B,C,D,E,F Suggested Timeframe (in blocks) 2 UNIT 4 – Applications of Derivatives Course Objective(s) Describe the Extreme Value Theorem in conjunction with identifying absolute and relative extrema on a given function Student Objectives • • • • • Exemplify the Mean Value Theorem and its Corollary, Rolle’s Theorem • • Explain the Extreme Value Theorem Distinguish between local and absolute maximums and minimums Illustrate points or intervals in which extrema do not exist Identify functions in which multiple extrema exist Define critical values as points in which a derivative either equals zero or does not exist Determine whether the Mean Value Theorem applies to a given function Use Rolle’s Theorem to determine where a derivative is equal to zero NJ CCCS Strands & Indicators 4.1 4.2 4.3 4.5 A,B,C C A,B,C,D A,B,C,D,E,F 4.1 4.2 4.3 4.5 A,B,C C A,B,C,D A,B,C,D,E,F Suggested Timeframe (in blocks) 4 1 Course Objective(s) Establish connections between a function and its first and second derivatives Student Objectives • • • • Sketch curves based on given information • • • Introduce the concept of the antiderivative • • • Use the derivative to...
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## This note was uploaded on 03/12/2010 for the course CALCULUS 1561234586 taught by Professor Zalla during the Spring '10 term at Air Force Institute of Technology, Ohio.

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