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Show that in Example $3, P(5,4)-P(5+h, 4+k)=2 h^{2}+7 k^{2} > 0$ and then explain why this proves $P$ has a maximum at $x=5$ and $y=4$

Calculus 3

Chapter 6

An Introduction to Functions of Several Variables

Section 5

Economic Applications

Partial Derivatives

Campbell University

Harvey Mudd College

Baylor University

University of Michigan - Ann Arbor

Lectures

12:15

In calculus, partial derivatives are derivatives of a function with respect to one or more of its arguments, where the other arguments are treated as constants. Partial derivatives contrast with total derivatives, which are derivatives of the total function with respect to all of its arguments.

04:14

00:29

Given $f(x)=a(x-h)^{2}+k,$…

01:09

Show that the maximum valu…

01:39

Let $f(x, y)=5-2 x+4 y-3 x…

00:57

Write each quadratic funct…

00:47

Yeah. The maximum value maximum value for F purpose one X equals two H. Because we have a smaller than zero. Right? So we have F max equals to eight times H minus h square plus K. He goes to okay, So the maximum value for for F you go to Okay.

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