Still Confused?

Try reviewing these fundamentals first

- Home
- Calculus 3
- Partial Derivative Applications

Still Confused?

Try reviewing these fundamentals first

Nope, got it.

That's the last lesson

Start now and get better math marks!

Get Started NowStart now and get better math marks!

Get Started NowStart now and get better math marks!

Get Started NowStart now and get better math marks!

Get Started Now- Intro Lesson: a7:19
- Intro Lesson: b2:23
- Intro Lesson: c25:37

This section is about optimizing a function, such that you find the absolute minimum and maximum on a certain region in $\mathbb{R}^2$.

- Closed Region: A region in $\mathbb{R}^2$ that includes its boundary
- Open Region: A region in $\mathbb{R}^2$ that excludes any of the boundary points
- Bounded Region: A region in $\mathbb{R}^2$ that is contained in a disk.

If a function $f(x,y)$ is continuous in a closed, bounded region $D$ in $\mathbb{R}^2$, then there are 2 points $(x_0,y_0)$ and $(x_1,y_1)$ where $f(x_0,y_0)$ is the absolute minimum and $f(x_1,y_1)$ is the absolute maximum of the function in the region $D$.

- Find all the critical points that are inside the region $D$.
- Find all the critical points on the boundary of region $D$.
- Find the function values for all the critical points
- Compare all the function values to see which is the smallest, and which is the largest. The smallest is the absolute minimum & and the largest is the absolute maximum.

- Introduction
**Local Minimum & Maximum of Multivariable Functions Overview:**a)__Types of Regions__- Open Region
- Closed Region
- Bounded Region
- Examples

b)__Extreme Value Theorem__- Closed, Bounded region $D$
- Absolute Minimum $f(x_0,y_0)$
- Absolute Maximum $f(x_1,y_1)$

c)__Steps to Finding Absolute Maximums & Minimums__- Find all critical points inside $D$
- Find all critical points on the boundary $D$
- Find the function values
- Compare, smallest $\to$ absolute min, largest $\to$ absolute max