AboutScotto Expertise Any kind of mathematics (calculus, analysis, game theory, linear approximation, finite differences, linear regression, linear programming, numerical analysis, probability, statistics, etc.).
I also have answered some questions in
Physics (mass, momentum, falling bodies),
Chemistry (charge, reactions, symbols, molecules), and
Biology.
Experience Experience in the area: I have tutored students in all areas of mathematics for over 20 years.
Education/Credentials: BSand MS in Mathematics from Oregon State University, where I completed sophomore course in Physics and Chemistry. I received both degrees with high honors.
Awards and Honors: I have passed Actuarial tests 100, 110, and 135.
Publications Maybe not a publication, but I have respond to well oveer 3000 questions on the PC.
That's around 2,000 in basic math and 1,000 in advanced math.
Education/Credentials I aquired well over 40 hours of upper division courses. This was well over the number that were required.
I graduated with honors in both my BS and MS degree from Oregon State University.
I was allowed to jump into a few junior level courses my sophomore year.
Awards and Honors I have been nominated as the expert of the month several times.
All of my scores right now are at least a 9.8 average (out of 10).
Past/Present Clients My past clients have been students at OSU, students at the college in South Seattle,
referals from a company, friends and aquantenances, people from my church, and people like you.
Question For a function such as y = ax + bz that depend on 2 or more variables (2 in this case), why is "Equating the partial differential of the function above with respect to each of independent variables (x and z in this case) and subsequently solving the thus generated simultaneous equations for the values of x and z" a sufficent condition to determine the maxima of the function.
Additionally, what is the corresponding sufficient condition to determine the minima of the same function?
Best regards
Deepak Agarwal
Answer The reason that this provides a solution is that the partial derivative in each variable is like if the other variable were a constant. To find the maximum with respect to one variable, you would take the derivative and set it equal to 0 as if the other variable were a constant. This is what the partial derivatives do with respect to x and z.
What is ended up with is two equations with two unknowns that are both equal to zero.
What this will tell you is where the maximum, minimum, and any inflection points are at.
The second partial for each variable will say whether it is a maximum, minimum, or inflection point in that direction.
