I have the function and I want to find the intervals where it increases or decreases. The problem is that when I find , which becomes . Once I put -2 on a number line, and find whether the numbers higher and lower than -2 produce positive or negative numbers when plugged into f′(x), I get both positives and negatives for different numbers when . For example, and .
I am not sure if this is because the function has a vertical asymptote at and a horizontal attribute at . If so, I'd like to know what I need to do to handle them.
How I found the first derivative:
How I found the asymptotes:
When you combine the fractions of f(x), . When set equal to zero, has an x-value of zero. Therefore, f(x) has a vertical asymptote at .
Once the fractions are combined, and when everything but the coefficients of the leading terms on the numerator and denominator are removed, . So f(x) has a horizontal asymptote at .
How I found the value of :
Add to both sides
Multiply both sides by .
Divide both sides by 6.