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In the previous example show that the demand levels produce a maximum at the critical values $x=a$ and $y=b,$ by showing that $P(a, b)-P(a+h, b+k)=2(h-k)^{2}+3 k^{2}$

Calculus 3

Chapter 6

An Introduction to Functions of Several Variables

Section 5

Economic Applications

Partial Derivatives

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Missouri State University

Campbell University

Harvey Mudd College

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

02:09

Suppose that $A, B,$ and $…

02:28

Consider the functions $f(…

01:05

03:31

Find the value(s) of $x$ t…

stoppable, 28 severe. Given a quadratic equation, eso were given a linear equation of relation that experts by sea, and we have to find them in Amman. Value off the X A squared plus b White Square. So let's from here we get the value of y as C minus six. So let's put the value off why here with Mrs B. Times C minus X couples were X squared plus B times. This will be sees where plus extra square minus two. Sears. So this will be equal to X square plus B. C's where we're opening of the brackets plus B X squared minus student B C X. Let's take extra square out from these troops were left with April's be Then we have, uh, this will be minus two times B c X plus B C squared. This is a parabola, which is opening up force. How do we know that? Because A and B are positive constants that is given in the in fact ABC. All three a positive, constant returns given in the question. So it's minimum by live a locker at its vortex, which is minus B over the way the value of B is menstrual BC The value off is a pres B. So from here begin to value off excess. BC over papers be on the value of why we will be C minus sexto. Let's find that C minus X X is BC who were a plus B So this becomes papers becomes here and this will be See Time's papers B minus B. C. So this becomes a C plus B C minus. B C or worry press B. These two get cancer, so we're left with a c O r a plus B, which is what we needed to proof. So these are the values of X sent wire for which excess weapons be by squares minimum.

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