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 I have finished most of my calculus homework assignment, but I can't seem
to figure out these problems. Hopefully you can help me out.
1) find the derivative of the functions
A) f(x) = ln(e^x^2+1)
B) f(x) = x^2e^x+e^x
2) using logarithmic differentiation to find the derivative of:
f(x) = (2x^3+1) (x^2+2)^3
3)find an equation of the tangent line to the graph of:
f(x) = x^2+2 ln x at it's inflection point. (Hint: f"(x))
4) find the absolute extrema of the function:
g(x) = (2x-1)e^-x on [0,infinity]
5) find the second derivative of:
y = e^3x ln 2x
6) solve for t:
5e^-2t = 6
Answer The derivative of ln(f(x)) is f'(x)/f(x).
The derivative of e^f(x) is f'(x)e^f(x).
The derivative is the slope at that point and a line can be found in the point-slope form using that x as x0 and f(x) as y0.
2) I'm not sure what logarithmic differentiation is.
3) Take the derivative and set it equal to 0 to find extreme points. The derivative of ln(x) is just 1/x. Take the second derivative and set it equal to 0 to find any inflection points.
4) Put in 0, take the limit as x goes to infinity, and find where the derivative is 0. Note that the derivative is like a product rule. If f(x)=g(x)^h(x), the derivative is g'(x)^h(x) + h'(x)(g(x)^h(x)).
5) This is a product rule. The derivative of e^(ax) is ae^(ax) and the derivative of ln(ax) is a/x. Remember the product rule:
(f(x)g(x))'=f(x)g'(x) + g(x)f'(x).
6) To both sides of the equation, do the following:
Divide by 5, take the natural ln, then divide by -2.
