*Typical phrases that indicate an Optimization problem include: Before you can look for that max/min value, you first have to develop the function that you’re going to optimize.There are thus two distinct Stages to completely solve these problems—something most students don’t initially realize [Ref]. Now maximize or minimize the function you just developed.Above, for instance, our equation for $A_\text$ has two variables, We can now make this substitution $h = \dfrac$ into the equation we developed earlier for the can’s total area: \[ \begin A_\text &= 2\pi r^2 2 \pi r h \[8px] &= 2\pi r^2 2 \pi r \left( \frac\right) \[8px] &= 2\pi r^2 2 \cancel \cancel \left(\frac\right) \[8px] &= 2\pi r^2 \frac \end \]We’re done with Step 3: we now have the function in terms of a single variable, , and we’ve dropped the subscript “total” from $A_\text$ since we no longer need it.*

Your first job is to develop a function that represents the quantity you want to optimize. Campbell for his specific research into students’ learning of Optimization: “College Student Difficulties with Applied Optimization Problems in Introductory Calculus,” unpublished masters thesis, The University of Maine, 2013.] access to step-by-step solutions to most textbook problems, probably including yours; (2) answers from a math expert about specific questions you have; AND (3) 30 minutes of free online tutoring.

One common application of calculus is calculating the minimum or maximum value of a function.

We’ve labeled the can’s height Having drawn the picture, the next step is to write an equation for the quantity we want to optimize.

Most frequently you’ll use your everyday knowledge of geometry for this step.

Let’s break ’em down and develop a strategy that you can use to solve them routinely for yourself.

Optimization problems will always ask you to maximize or minimize some quantity, having described the situation using words (instead of immediately giving you a function to max/minimize).

In this problem, for instance, we want to minimize the cost of constructing the can, which means we want to use .

So let’s write an equation for that total surface area:\begin A_\text &= A_\text A_\text A_\text \[8px] &= \pi r^2 2\pi r h \pi r^2 \[8px] &= 2\pi r^2 2 \pi r h \end That’s it; you’re done with Step 2!

Notice, by the way, that so far in our solution we haven’t used any Calculus at all.

That will always be the case when you solve an Optimization problem: you don’t use Calculus until you come to Stage II.

## Comments Solving Optimization Problems In Calculus

## Optimization with Calculus 1 - YouTube

Jun 15, 2008. Optimization with Calculus 1. 581K views. 1.6K. 59. Share. Save. Report. Optimization Problems. The Organic Chemistry Tutor. 44K views.…

## Optimization Problems - Mathematics LibreTexts

Apr 27, 2019. One common application of calculus is calculating the minimum or maximum. Solving Optimization Problems over a Closed, Bounded Interval.…

## How to Solve Optimization Problems in Calculus -

Jul 7, 2016. How to Solve Optimization Problems in Calculus. Optimization problems will always ask you to maximize or minimize some quantity, having.…

## Optimization Calculus - Fence Problems, Cylinder, Volume of.

Nov 19, 2016. This calculus video tutorial explains how to solve optimization problems such as the fence problem along the river, fence problem with cost.…

## Steps for Optimization Problems - CMU Math

Optimization problems often involve geometry. Draw a picture of the situation. Solve each of the constraint equations for one of the variables and substitute this.…

## How to solve optimization problems in calculus Question 1.

Aug 17, 2017. Brought to you by https//🤔 Still stuck in math? Visit https//StudyForce.com/index.php?board=33.0 to start asking questions.…

## Optimization box volume Part 1 video Khan Academy

Solving optimization problems. Optimization area of triangle & square Part 1. And before we do it analytically with a bit of calculus, let's do it graphically.…

## Optimization - Calculus KristaKingMath - YouTube

Jun 5, 2012. Optimization - Calculus KristaKingMath. Understand one of the hardest and most common applications of derivatives, optimization and it's applications. Optimization Calculus - Fence Problems, Cylinder, Volume of Box, Minimum Distance. Solving Derivatives KristaKingMath - Duration.…

## Calculus I - Optimization - Pauls Online Math Notes

May 30, 2018. In optimization problems we are looking for the largest value or the smallest value that a function can take. We saw how to solve one kind of.…

## Calculus - Solving Optimization Problems - YouTube

Jan 20, 2017. Correction 3180=540 answer should be ±16.43 This lesson shows how to solve problems involving optimization. Optimization.…