Calculus: Relative Extrema Introductional Worksheet

Calculus: Relative Extrema Introductional Worksheet
Calculus: Relative Extrema Introductional Worksheet
Calculus: Relative Extrema Introductional Worksheet
Calculus: Relative Extrema Introductional Worksheet
Calculus: Relative Extrema Introductional Worksheet
Calculus: Relative Extrema Introductional Worksheet
Calculus: Relative Extrema Introductional Worksheet
Calculus: Relative Extrema Introductional Worksheet
File Type

Word Document File

(91 KB|2 pages)
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Standards
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  • StandardsNEW
This worksheet is designed to be used as a quick, in-class discovery/formative assignment. Typically, students will complete the assignment, in 10 to 15 minutes. Students will look at a visual representation of a function graphed with its derivative, answer a couple questions about the graph, and discover the means to finding relative extrema.

***The preview has the equations blacked out, but the copy you purchase contains the actual equations with an answer key. The file is a word document, so teachers have the ability to edit the document to further meet the needs of their class.
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Look for and make use of structure. Mathematically proficient students look closely to discern a pattern or structure. Young students, for example, might notice that three and seven more is the same amount as seven and three more, or they may sort a collection of shapes according to how many sides the shapes have. Later, students will see 7 Γ— 8 equals the well remembered 7 Γ— 5 + 7 Γ— 3, in preparation for learning about the distributive property. In the expression π‘₯Β² + 9π‘₯ + 14, older students can see the 14 as 2 Γ— 7 and the 9 as 2 + 7. They recognize the significance of an existing line in a geometric figure and can use the strategy of drawing an auxiliary line for solving problems. They also can step back for an overview and shift perspective. They can see complicated things, such as some algebraic expressions, as single objects or as being composed of several objects. For example, they can see 5 – 3(π‘₯ – 𝑦)Β² as 5 minus a positive number times a square and use that to realize that its value cannot be more than 5 for any real numbers π‘₯ and 𝑦.
Model with mathematics. Mathematically proficient students can apply the mathematics they know to solve problems arising in everyday life, society, and the workplace. In early grades, this might be as simple as writing an addition equation to describe a situation. In middle grades, a student might apply proportional reasoning to plan a school event or analyze a problem in the community. By high school, a student might use geometry to solve a design problem or use a function to describe how one quantity of interest depends on another. Mathematically proficient students who can apply what they know are comfortable making assumptions and approximations to simplify a complicated situation, realizing that these may need revision later. They are able to identify important quantities in a practical situation and map their relationships using such tools as diagrams, two-way tables, graphs, flowcharts and formulas. They can analyze those relationships mathematically to draw conclusions. They routinely interpret their mathematical results in the context of the situation and reflect on whether the results make sense, possibly improving the model if it has not served its purpose.
Reason abstractly and quantitatively. Mathematically proficient students make sense of quantities and their relationships in problem situations. They bring two complementary abilities to bear on problems involving quantitative relationships: the ability to decontextualize-to abstract a given situation and represent it symbolically and manipulate the representing symbols as if they have a life of their own, without necessarily attending to their referents-and the ability to contextualize, to pause as needed during the manipulation process in order to probe into the referents for the symbols involved. Quantitative reasoning entails habits of creating a coherent representation of the problem at hand; considering the units involved; attending to the meaning of quantities, not just how to compute them; and knowing and flexibly using different properties of operations and objects.
Graph linear and quadratic functions and show intercepts, maxima, and minima.
Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph.
Total Pages
2 pages
Answer Key
Included
Teaching Duration
30 minutes
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