calc
posted by Paisley .
f(x)= x^3/x^216 defined on [19, 16]
How would you find the vertical asymptopes? and the inflection point?
I think you take the derivative and set it to zero? but i cant figure out the correct derivative or something??

assume you mean (x^216) on the bottom
vertical asymptotes are where the denominator goes to zero
that is when x = 4 and x = +4
derivative of fraction =
(bottom * derivative of top  top * derivative of bottom)
all over bottom squared
[(x^216)*3 x^2  x^3(2x) ]/bottom^2
look for zeros of numerator
3 x^4  48 x^2  2 x^4
=x^4  48 x^2
= x^2 (x^248)
= x^2 (xsqrt 48)(x+sqrt 48)
so zero at sqrt 48, 0 and + sqrt 48
check my arithmetic, I did that fast. 
by the way sqrt 48 = 4 sqrt 3
Respond to this Question
Similar Questions

calc
one more question!! what values of c deos the polynomial f(x) = x^4 + cx^3 + x^2 have two inflection points? 
Calc Help
Find two functions that this could be the derivative of: y'=4x+7 Remember the derivative of any constant is zero. take its antiderivative i suppose... y= 2x^2 + 7x + any number 
calc
derivative of (x^3/6)+(1/2x)? i got (x^2/2)(1/2x^2) is that correct? 
Calculus> bobpursley
How do you get m=0? from taking the second derivative? 
Calc
1. Find values of a,b,c, and d such that g(x) = a(x^3)+b(x^2)+cx+d has a local maximum at (2,4) and a local minimum at (0,0) 2. Need someone to explain this. Graph a function f(x) for which: f(3)=f(5)=0 f'(x)<0 if x<4 f'(4)=0 … 
calc
The function f is defined by f(x) = x^3  x^2  4x + 4 The point (a,b) is on the graph of f and the line tangent to the graph at (a,b) passes through the point (0, 8) which is not on the graph of f. Find the values of a and b. I have … 
Calc
Profit=p(p^2+33p+9)9(p^2+33p+9)+100 How do I simplify this so I can take the derivative For Further Reading * Calc  Michael, Sunday, November 25, 2007 at 4:17pm Profit=p(p^2+33p+9)9(p^2+33p+9)+100 p(p^2 + 33p + 9) Just distribute … 
calc.
I'm having a lot of trouble with this problem: Sketch the graph and show all local extrema and inflections. f(x)= (x^(1/3)) ((x^2)175) I graphed the function on my graphing calculator and found the shape. I also found the first derivative: … 
Calc I
if f(t)=sqrt(4t+1) find f''(2) I got the first derivative to be: 1/2(4t1)^1/2 * 4t^3 and i'm trying to figure out if i need the product rule again to find the second derivative 1t^3(4t1)^3/2 * 4t^3 The answer if 4/27 and I'm … 
Calculus,Stationary Points,First derivative test
Good afternoon, I need a bit of help. So ive got my first derivative which is 6x^26x12 and the stationary points ive found are x=1 and x=2 at which points the value of the derivative is zero. So im attempting to classify the points. …