Optimization Calculus Worksheet Pdf

[Kevin]

Themonomial is the basic building block of the polynomial. It can be either a constant or a constant with any variables. What happens when there is more than one monomial, like we have in the linear equation?

Based on the graph, it is easy to pinpoint where the maximum, or vertex, of the parabola is. However, what if we have more than one point that can be the maximum or minimum?

The absolute extrema are defined as the extrema that, within the domain specified, are the highest or lowest. In other words, when we look at a specific range of values for a function, the absolute extrema are the highest or lowest points in that range.

Optimization in calculus involves finding the absolute extrema within a range. What this means is that we want to perform a first derivative test to find the absolute minimum or maximum. We do this for two reasons.

Another common problem in optimization deals with cylinders. For example, you have 300 millilitres of juice. You need to find the dimensions of a cylindrical can that would minimize the cost of producing that can.

We want to minimize the surface area. Since we know the final volume that has to fit into the cylinder, we can replace this in the formula. Then, we re-arrange the formula so that only one variable is on each side.

Description: Students will carry out an application of calculus that is typical of optimization problems. Students will calculate the minimum cost of producing a rectangular storage container given the volume of the container and the cost of materials required for the sides and base of the container. Worksheet doc.

Description: We outline a method in which a spring can be used to simultaneously determine the mass of an object in outer space and the spring constant. In outer space, it is important for astronauts to know their mass, an indicator of health. Website.

Timing Suggestion: It could take place at any time after derivatives and max/min are covered (after Session 13). The activity takes one class period and up to an hour or so to finish after class.

Timing Suggestion: It could take place at any time after derivatives and max/min are covered (after Session 13). The activity takes one class period and up to an hour or so to finish after class.

Description: In this application students will be given two real situations. Students will be provided with an internet link which will provide them single tax filing and married filing jointly brackets with their state income tax owed. For example, using this tax information for New York State, students will write a piecewise function in terms of x for New York State tax for 2019. The written piece wise function will be graphed using Desmos. Key concepts included in this application are: the domain and range of the function in interval notation, the constant interval, any points of discontinuity and their location, maximum and/or minimum value, and the interval of decrease or increase. Worksheet and rubric docs.

Timing Suggestion: This application will be used after the One-Sided Limits or the Interpretation of the derivative section are taught (Sessions 3 and 4). The in class part would take 20-25 minutes, while the out of class time would take between 40-45 minutes.

NOTE: This site is a repository of information and is not intended for direct communication between students and faculty. If you are a student in MAT 1475, your professor will let you know how and where to reach them online.

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