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 Given the following function, state the domain, all asymptotes, intercepts, relative extrema and inflection points.
h(x)=(4-x^2)/(x^2+1)
I know I have to use 2nd derivative to find the inflection point but I am stuck. Need help asap :D
thanks
Answer The function is f(x) = (4 - x²)/(x² + 1).
To find the derivative, use the quotient rule.
That is, (lo d hi - hi d low)/lo sqaured.
The first derivative is f'(x) = ((x²+1)(-2x) - (4-x²)(2x))/(x²+1)².
Simplifying this gives (-2x³ - 2x - 8x + 2x³)/(x² + 1)².
Noticing the cubes in the numerator cancel, we are left with
-10x/(x² + 1)².
Use the quotient rule again to find f"(x).
That is, f"(x) = ((x²+1)²(-10) -- 10x(2(x²+1)2x))/(x²+1)^4.
Simplifying again gives us
f"(x) = (-10(x^4 + 2x² + 1) + 10x(4x^3 + 4x))/(x²+1)^4, which is
= 10(-x^4 + 4x^3 - 2x² + 4x - 1)/(x²+1)^4.
Where this function is 0 is where the points of inflection are at.
To find these points, set -x^4 + 4x^3 - 2x² + 4x - 1 = 0 and solve.
A good way to do this would be to use a spreadsheet and put the x values in column A and then the y values in column B.
Say A1 contains an X value.
Then B1 would have =-1+A1*(4+A1*(-2+A1*(4-A1))).
Copy B1 down to several rows and try various values column A.
