# Mcv4u optimization

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

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Unit 5: Related Rates and Optimization (2-3 weeks) Unit 6: Curve Sketching (1-2 weeks) ***MCV4U is completed at this point. The 70% term work will be based on the evaluations covered. The Final Exam will be based on curriculum covered to this point. Unit 7: Integrals and the Fundamental Theorem of Calculus (3-4 weeks) Optimization * 1. An open box is to be made from a 16 inch by 30 inch piece of cardboard by cutting out squares from the four corners and bending up the sides. What size should the squares be to obtain a box with the largest volume? 2. A closed cylindrical can is to hold 1 L (1000 cm3) of liquid. How should you choose the
Open ended Math Projects and Lessons Due to popular demand I have created a "Table of Contents" for my Open ended Math Projects. Below you will find the link, and which Math topic it could be used for. MCV4U Final Project Instructions and Rubric Name:_____ For your final project, you will incorporate what you have learned in the Calculus component of the course into a creative representation. Some projects in the past have included music videos, story books, short movies, etc. MCV4U. MCV4U – Unit 1 – Limits; MCV4U – Unit 2 – Derivatives; MCV4U – Curve Sketching and Optimization; MCV4U – Derivatives of Exp, Log, Trig Functions; MCV4U – Vectors and Applications; MCV4U – Equations and Intersections of Lines; MCV4U – Equations and Intersections of Planes; MCR3U. MCR3U – Unit 0 – Review

Page. 1 / 16 Quest on Optimization Problems . Read. 4.1 Instantaneous Rates of Change of Sinusoidal Functions. on your own . 4.2 Derivatives of the Sine and Cosine Functions . Derivatives of Sine Functions . Proof of . Limit of (sin h)/h as h approaches 0 = 1 . 4.3 Differentiation Rules for Sinusoidal. Functions. 4.4 Applications of Sinusoidal Functions
Grade 12 – Calculus and Vectors Curve Sketching Test Interval of Increase and Decrease A function is increasing if the slope of the tangent is positive over the entire interval … A brief introduction to matrix algebra, linear algebra, and applications. Topics include systems of linear equations, matrix algebra, determinants, the vector spaces Rn and their subspaces, bases, co‐ordinates, orthogonalization, linear transformations, eigenvectors, diagonalization of symmetric matrices, quadratic forms.

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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.