Look for and express regularity in repeated reasoning. 6. Analyze graphs of Investigate and generalize the Calculus: Concepts & Contexts 1. Make sense of problems and persevere relationship between function and its first the graph of f and f'. Section 2.8 in solving them. Investigate and generalize the and second 2. Reason abstractly and quantitatively. relationship between the graph of f' and f"" derivatives and 3. Construct viable arguments and critique the graph of a function estimate the distinguish the reasoning of others. derivative at various given points. characteristics of 4. with math. the graph of a function, create a each. 5. Use appropriate tools strategically. District constructed materials sketch of its derivative function 6. Attend to precision. an equation for a function (f(x)), find 7. Look for and make use of structure. the derivative (f (x)) algebraically ′ 8. Look for and express regularity in a sketch of a function, identify where it repeated reasoning. is not differentiable and why a sketch of a function and its first and second derivatives, distinguish between the two graphs. Learning Objective Standards for Mathematical Practice The student will… Content Outline Instructional Materials 7a. Connect and apply Calculus: Concepts & Contexts 1. Make of problems and persevere in how derivatives and the antiderivative to antiderivatives related to each other Section 2.9 solving them. graphically the derivative 2. Reason abstractly and quantitatively. the graph of a derivative function, 3. Construct viable arguments and critique identify the places where the function is 7b. Interpret graphs of the reasoning of others. increasing/decreasing, concave up/down, the derivative of a 4. with math. local max/min, points of inflection function 5. Use appropriate tools strategically. District constructed materials a graph of a function given 6. Attend to precision. information about its derivative 7. Look for and make use of structure. 8. Look for and express regularity in repeated reasoning.
Look for and express regularity in repeated reasoning. 6. Analyze graphs of function and its first and second derivatives and distinguish characteristics of each. Investigate and generalize the relationship between the graph of f and f'. Investigate and generalize the relationship between the graph of f' and f"" the graph of a function estimate the derivative at various given points. the graph of a function, create a sketch of its derivative function an equation for a function (f(x)), find the derivative (f ′ (x)) algebraically a sketch of a function, identify where it is not differentiable and why a sketch of a function and its first and second derivatives, distinguish between the two graphs. Calculus: Concepts & Contexts Section 2.8 District constructed materials 1. Make sense of problems and persevere in solving them. 2. Reason abstractly and quantitatively. 3. Construct viable arguments and critique the reasoning of others. 4. with math. 5. Use appropriate tools strategically. 6. Attend to precision. 7. Look for and make use of structure. 8. Look for and express regularity in repeated reasoning. Learning Objective The student will… Content Outline Instructional Materials Standards for Mathematical Practice 7a. Connect and apply the antiderivative to the derivative 7b. Interpret graphs of the derivative of a function how derivatives and antiderivatives related to each other graphically the graph of a derivative function, identify the places where the function is increasing/decreasing, concave up/down, local max/min, points of inflection a graph of a function given information about its derivative Calculus: Concepts & Contexts Section 2.9 District constructed materials 1. Make of problems and persevere in solving them. 2. Reason abstractly and quantitatively. 3. Construct viable arguments and critique the reasoning of others. 4. with math. 5. Use appropriate tools strategically. 6. Attend to precision. 7. Look for and make use of structure. 8. Look for and express regularity in repeated reasoning.
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