Calculus Optimization Worksheet A Rain Gutter Is To Be Constructed

A rain gutter is to be constructed from a metal sheet of width 30cm by bending up one third of the sheet on each side by an angle theta from the horizontal theta zero represents the unbent sheet.

Calculus optimization worksheet a rain gutter is to be constructed.

1 a company has started selling a new type of smartphone at the price of 110 0 05 x where x is the number of smartphones manufactured per day. Determine what theta should be chosen so that the gutter will carry the most water when it is full. Differential calculus published in vacaville california usa a rain gutter is to be constructed from a metal sheet of width 30 cm. A rain gutter is to be constructed from a metal sheet of width 30 cm by bending up one third of the sheet on each side through an angle θ.

How should θ be chosen so that the gutter will carry the maximum amount of water. A rain gutter is to be constructed from a metal sheet of width 30 cm by bending up one third of the sheet on each side through an angle theta. You da real mvps. Verify if it is a maximum or minimum using the 2nd derivative test when easy otherwise use the 1st derivative test.

The parts for each smartphone cost 50 and the labor and overhead for running the plant cost 6000 per day. 1 draw a diagram depicting the problem scenario but show only the essentials. Here are the steps in the optimization problem solving process. Maximizing or minimizing some quantity so as to optimize some outcome calculus is the principal tool in finding the best solutions to these practical problems.

Textbook solution for single variable calculus 8th edition james stewart chapter 3 7 problem 76e. Optimization problems practice solve each optimization problem. How should theta be chosen so that the gutter will carry the maximum amount of water. Optimization problems name calculus ab for each of the following define your variables write an equation representing the quantity to be maximized or minimized and solve the problem.

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