Calculus Optimization Worksheet A Rain Gutter Is To Be Constructed

Verify if it is a maximum or minimum using the 2nd derivative test when easy otherwise use the 1st derivative test.

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. We need to begin by constructing a function which gives the area of the gutter in terms of theta. Textbook solution for single variable calculus 8th edition james stewart chapter 3 7 problem 76e. You da real mvps.

1 per month helps. 1 draw a diagram depicting the problem scenario but show only the essentials. To calculate the area split the cross section of the gutter into two triangles and a rectangle. 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.

Most real world problems are concerned with. How should θ be chosen so that the gutter will carry the maximum amount of water. Thanks to all of you who support me on patreon. 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.

The parts for each smartphone cost 50 and the labor and overhead for running the plant cost 6000 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. Determine what theta should be chosen so that the gutter will carry the most water when it is full. 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.

Differential calculus published in vacaville california usa a rain gutter is to be constructed from a metal sheet of width 30 cm. 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. We have step by step solutions for your textbooks written by bartleby experts. Here are the steps in the optimization problem solving process.