# math

posted by .

f(x)=x/(x^2+x-2)
find:
x intercepts
vertical asymptotes
horizontal/slant asymptotes
derivative
second derivative
increasing interval
decreasing interval
concave up interval
concave down interval

• math -

You should be able to do some of these yourself. If not, you are behind class level and would benefit from private tutoring.

The x intercept(s) occur where f(x) = 0. That can only happen at when the numerator is zero. In other words, at x = 0.

Vertical asymptotes occur wherever the denominator of f(x) is zero. Note that the denominator of f(x) can be written (x+2)(x-1). That should tell you where the asymptotes are.

For the derivative of
f(x) = x/(x^2 +x -2), let
u(x) = x and v(x) = x^2 +x -2
and use the rule for the derivative of the fraction u(x)/v(x), which you should know.
f'(x) = (v*u' - u*v')/v^2
= [x^2 +x -2 -x*(2x +1)]/(x^2 +x -2)^2
= (-x^2 -2)/(x^2 +x -2)^2

Use the same "u/v" rule for the second derivative.

Plotting the f(x) function yourself should help for the last four questions. "Increasing up or down" is determined by the sign of f'(x).
"Concave up or down" is determined by the sign of f''(x), the second derivative.

## Similar Questions

1. ### Calc

f(x) = x^2 / (x - 7)^2 (a) Find the vertical and horizontal asymptotes. x= y= (b) Find the interval where the function is increasing. Find the intervals where the function is decreasing. (Enter the interval that contains smaller numbers …
2. ### Calculus (pleas help!!!)

Please answer the following questions about the function f(x)=e^(-0.5x^2) Instructions: If you are asked to find x- or y-values, enter either a number, a list of numbers separated by commas, or None if there aren't any solutions. Use …
3. ### Calculus (pleas help!!!)

Please answer the following questions about the function f(x)=e^(-0.5x^2) Instructions: If you are asked to find x- or y-values, enter either a number, a list of numbers separated by commas, or None if there aren't any solutions. Use …
4. ### Calculus (urgent!!)

Please answer the following questions about the function f(x)=e^(-0.5x^2) Instructions: If you are asked to find x- or y-values, enter either a number, a list of numbers separated by commas, or None if there aren't any solutions. Use …
5. ### math

f(x)=x^3+6x^2+9x find: x intercepts vertical asymptotes horizontal/slant asymptotes derivative second derivative increasing interval decreasing interval concave up interval concave down interval
6. ### math

(x^3+7x+12)/(x-4) find: x intercepts vertical asymptotes horizontal/slant asymptotes derivative second derivative increasing interval decreasing interval concave up interval concave down interval
7. ### Please check my Calculus

1. Given f(x)=-6/x, choose the correct statement A. The graph of f is concave upward on the interval (negative infinity, 0) B. The graph of f is concave downward on the interval (negative infinity, 0) C. The graph of f is concave upward …
8. ### Calculus

Consider the following function f(x)=x^2/[x^2-9] f(x) is increasing on the interval(s) f(x) is decreasing on the interval(s) f(x) has 2 vertical asymptotes x= f(x) is concave up on the interval(s) f(x) concave down on the interval(s) …