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 could you give me the reason for choosing f'(x)=0;if f(X)is a real function?and also could you give me the proof of having
f'(C)=f(b)-f(a)/b-a in mean value theorem
Answer The reason for choosing f'(x)=0 if for finding the extreme points of the function since when an extreme point is reached, continuous functions go from a slope up to a slope down, making it 0 at the extreme point.
The mean value theorem assumes the function and its derivatives are both continuous over the interval [a,b] and the C is some point in between a and b. f'(C) is the slope of a straight line from (a,f(a)) to (b,f(b)).
Let's suppose that at the start the graph slopes up faster at a than the average slope. To come into b at f(b), the function needs to have a lesser slope than the average somewhere. Since the derivative is assumed to be continuous, then at some point in the interval the slope needs to be the average slope since it was greater at one end and lesser at the other.
If the graph slopes up slower than the average change at the start, at some point in the middle it must slope up faster to reach (b,f(b)). It must therefore (from continuity) be equal the average slope somewhere in the middle.
If the graph slope is equal to the average slope at the left side, we're done before we started.
