# Math

posted by .

Given [(x-5)/(x-3)]^2 . Find any stationary points and any points of inflection. Also find any horizontal and
vertical asymptotes.

• Math -

Stationary points are points at which f'(x)=0 AND f"(x)=0.
Vertical asymptote is where the denominator becomes zero.
Horizontal asymptote is the limit when x->∞ or x->-∞, if the limit is defined.

• Math -

could you please solve the problem completely .. i am still confused.
Thanks.

• Math -

Denominator becomes zero when x=3, therefore vertical asymptote is a x=3.

The limit of f(x)=[(x-5)/(x-3)]^2 as x->±∞ is 1, so the horizontal asymptote is at y=1.

Since f'(5)=0 and f"(6)=0, there are no stationary points, just a minimum at x=5.
There is a point of inflection at x=6 (where f"(6)=0).

You will need to take the time to calculate f'(x) and f"(x) from f(x), and hence sketch the graph of f(x).

A sketch of the graph can be seen here:
http://img718.imageshack.us/img718/4296/1292787276.png

## Similar Questions

1. ### calc

Given [(x-5)/(x-3)]^2 . Find any stationary points and any points of inflection. Also find any horizontal and vertical asymptotes.
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. ### Calculus

Sketch the graph of f(x)=-x^4 + 4x^3 - 16x + 16: Find the critical points, concave up/down, inflection points, vertical asymptotes and horizontal asymptotes.
6. ### Calculus

Sketch the graph of f(x)=x+2/x-4. Find the vertical and horizontal asymptotes, critical points, concave up/down, and inflection points.
7. ### Calculus

Sketch the graph of f(x)=(x^2 + 2)/x^2 - 4. Fund the vertical and horizontal asymptotes, the critical points, the points of inflection and the concavity.
8. ### math calculus

For the function: f(x)= 2+x-x^2/ (x-1)^2 ; f'(x)= x-5/(x-1)^3 ; f''(x)=2x-14/(x-1)^4 a)find vertical and horizontal asymptotes. Examine vertical asymptote on either side of discontinuity. b)find any local extrema c)find points of inflection
9. ### APCalculus

For the function y=4-2x^2+1/6x^4 find the following: Domain x and y intercepts Vertical asymptotes Horizontal asymptotes Symmetry F'(x) Critical numbers Increasing f(x) Decreasing f(x) Extrema F"(x) Possible points of inflection Concave …
10. ### APCalculus

For the function y=2sin(x)-cos^2(x) on [0, 2pi] find the following: Domain x and y intercepts Vertical asymptotes Horizontal asymptotes Symmetry F'(x) Critical numbers Increasing f(x) Decreasing f(x) Extrema F"(x) Possible points of …

More Similar Questions