Posted by Anonymous on Friday, October 29, 2010 at 6:25am.
Consider the function f(x) = x/(x1)
Are there any turning points? Explain how this could help you graph f(x) for large values of x?
Ans: turning points is another word for checking the concavity, and therefore i find the second derivative and equate it to zero and see where it is concave up and down, using that information i can know when the graph is increasing or decreasing, with its end behaviors near the asymptote
I get the second derivative as f''(x) = 2/(x1)^3. If f''(x) = 0 then there are no solutions, hence there are no turning points.
Am i correct? But how does that help me graph f(x) for large values.

Math  Simple rational functions (check)  Reiny, Friday, October 29, 2010 at 8:02am
"Turning points" is the same as maximum or minimum points, and we find them by setting the first derivative equal to zero.
Setting the second derivative equal to zero gives us
"points of inflection"
This page summarizes it for you
http://www.teacherschoice.com.au/Maths_Library/Calculus/stationary_points.htm
In most cases you can use common sense to find what happens to the graph for large values of x, by merely considering the numbers involved.
in your case consider a large x like x = 1000
the denominator is simply one less than the top, so we get 1000/999 which is barely above 1
the larger the x the closer we get to 1, but still above it
so for x > + infinity, f(x) = 1+
similarly for huge negative x's, e.g. x = 1000
we get 1000/1001 which is barely below 1
so as x >  infinity , f(x) > 1

Math  Simple rational functions (check)  shila, Friday, October 29, 2010 at 1:17pm
what is the anwser to this input output table here it is input(x)2,1,0,1,2,3,here is the output(y)1,1,3,5,7,9,

Math  Simple rational functions (check)  Valencia, Thursday, February 9, 2012 at 5:16pm
3(x^2x6)/4(x^29) what is the domain?
Answer This Question
Related Questions
 Math  Simple rational Function (check)  Consider the function f(x) = x/(x1) ...
 Precalculus  Number of possible turning points in the following equation f(x)=...
 Math  Determine the maximum and minimum number of turning points for the ...
 precalculus  Determine the maximum and minimum number of turning points for the...
 precalculus  analyzethe graph of the function Find the x and yintercepts. (b...
 Functions/End behavior  f(x)=x^2(x^22)(x+2) Determine the end behavior, find ...
 math pre calculus  find the following for the function f(x)=(x+5)^2(x2)^2 a....
 College alg  Analyze the graph of the following function as follows: (a) Find ...
 calculus  given the following function find, a. zeros and the multiplicity of ...
 calculuscan someone please help me with this ques  Given the following ...
More Related Questions