# Thread: function of x help again

1. ## function of x help again

i have the function f(x) = x^2+3(x)/2(x)^2+6(x)+4. I need to calculate the intervals on which f is increasing or decreasing, the nature of any stationary points and the value of f at each of these points. I also need to work out the asymptotic behaviour of f. I dont know where to begin!!! Please can anyone help.

2. What is the equation here?

$f(x)= x^2+\frac{3x}{2x^2}+6x+4$
or

$f(x)= \frac{x^2+3x}{2x^2+6x+4}$

3. Its the bottom equation

4. Ok, first thing to do is factorise the denominator.

What do you get?

5. so far I have factorised the denominator of f(x) to (2x+4)(x+1) giving x =-1 and x = -2. Which gave me intervals of (-infinity,-2) where f is positive, (-2,-1) where f is negative and (-1,infinity) where f is positive.

I determined that the function was neither od or even as no features were symmetrical.

Found the y intercept to be 0 and the x-intercepts to be 0 and -3

and now Im at a stand still and dont know what to do next?

6. Sounds good, you need to find where the function is increasing/decreasing so take the derivative using the quoient rule.

What do you get?