3.3 3.4 Optimization ©2010 Iulia & Teodoru Gugoiu - Page 2 of 4 C Maximize the Volume given the Shape and Area Ex 2. If 2700cm2 of material is available to make a box with a square base and an open top, find the dimensions (length, width, and height) of the box that give the largest volume of the box. What is the maximum volume of the box? A rectangular storage container with an open top needs to have a volume of 10 cubic meters. The length of its base is twice the width. Material for the base costs $10 per square meter.

Curve Sketching Whether we are interested in a function as a purely mathematical object or in connection with some application to the real world, it is often useful to know what the graph of the function looks like. We can obtain a good picture of the graph using certain crucial information provided by derivatives of the function and certain ... Ontario eSecondary School C ourse Outline – MCV4U: Calculus and Vectors, Grade 12, University preparation Page 5 of 10 Research i s completed in an online environment by teaching the students first about plagiarism rules and

Page. 1 / 16 MCV4U Calculus and Vectors 12. Course Title: Calculus and Vectors, Grade 12, University Preparation (MCV4U) Course Name: Calculus and Vectors Course Code: MCV4U Grade: 12 Course Type: University Preparation Credit Value: 1.0 Prerequisite: Advanced Functions MHF4U, may be taken concurrently

Curve Sketching Date_____ Period____ For each problem, find the: x and y intercepts, x-coordinates of the critical points, open intervals where the function is increasing and decreasing, x-coordinates of the inflection points, open intervals where the function is concave up and concave down, and relative minima and maxima.