Sign charts to organize information about a function

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Unformatted text preview: identify the interval over which a function is increasing, decreasing, or equal to zero Describe a local maximum as the point in which the derivative changes from positive to negative Describe a local minimum as the point in which the derivative changes from negative to positive Use the second derivative to determine concavity Construct sign charts to organize information about a function and its derivative Sketch a function given information about the derivative or the graph of the derivative itself Justify conclusions about the original function and its extrema using calculus concepts Recall the relationships between a function and the first and second derivative Practice using the general formula for antiderivative: f(x) = x n+1/(n +1) Apply physics applications (i.e.velocity) to finding position functions given initial conditions NJ CCCS Strands & Indicators Suggested Timeframe (in blocks) 3 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 3 4.1 4.2 4.3 4.5 A,B,C C A,B,C,D A,B,C,D,E,F 1 Course Objective(s) Present optimization as an application of differentiation Student Objectives • • • Introduce related rates as a second application of derivatives • • • • • NJ CCCS Strands & Indicators Interpret real-world examples in economics, manufacturing, shipping, land surveying and marketing Create equations to minimize or maximize a value or number of objects, and apply the concept of “setting the derivative equal to zero” to identify maximum and minimum points Interpret results in the context of the problem 4.1 4.2 4.3 4.5 A,B,C A1,A2,C,D, E A,B,C,D A,B,C,D,E,F Identify “common” real-world problems in which related rates are present: i.e. ladder sliding down a wall, baseball player running between bases, hot air balloon rising, vehicles commuting to and from various location Identify all variables in the problem, and determine the relationship between them Recall the Chain Rule and implicit differentiation View each variable as dependent with individual rates Solve for rates and distances with appropriate units of measure, and interpret results 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) 3 3 UNIT 5 – Integration Course Objective(s) Introduce integration by estimating “area under a curve” Student Objectives • • • • Describe the indefinite integral and all associated concepts • • • Estimate area using Rectangular Approximation: Right and Left Riemann Sums and ‘Midpoint’ Approximation Estimate area using Trapezoidal Approximation Given the actual area, find the error using the above methods as well as Simpson’s Rule Develop and comprehend Riemann’s summation for actual area: the number of rectangular subdivisions approaches infinity and the width of each rectangle (change in x) approaches ‘0’ Connect Riemann’s summation to Leibnitz’s integral notation Understand all components of the indefinite integral: limits, integrand, dx, “+ C” Describe basic integration in terms of the “antiderivative” and apply properties: using constants, splitting an integral, reversing limits, etc. NJ CCCS Strands & Indicators 4.1 4,2 4.3 4.5 A,B,C A1,A3,C,D, A,B,C,D A,B,C,D,E,F 4.1...
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