Calculus Optimization Worksheet A Rain Gutter Is To Be Constructed

The parts for each smartphone cost 50 and the labor and overhead for running the plant cost 6000 per day.

Calculus optimization worksheet a rain gutter is to be constructed.

How should θ be chosen so that the gutter will carry the maximum amount of water. Textbook solution for single variable calculus 8th edition james stewart chapter 3 7 problem 76e. Here are the steps in the optimization problem solving process. We need to begin by constructing a function which gives the area of the gutter in terms of theta.

Determine what theta should be chosen so that the gutter will carry the most water when it is full. Thanks to all of you who support me on patreon. You da real mvps. 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.

By bending up one third of the sheet on each side through an angle θ. Verify if it is a maximum or minimum using the 2nd derivative test when easy otherwise use the 1st derivative test. Optimization problems practice solve each optimization problem. Most real world problems are concerned with.

1 draw a diagram depicting the problem scenario but show only the essentials. 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. 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. 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.

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. How should theta be chosen so that the gutter will carry the maximum amount of water. We have step by step solutions for your textbooks written by bartleby experts. 1 per month helps.