Expert: Paul Klarreich - 2/14/2009

Question
1.) Determine the following about the graph of the equation y= (8/x^3)-(6/x).
a.) Is the graph symmetric with respect to the 1.) X-axis? 2.) Y-axis? 3.) Origin?
b.) Find the x-coordinates of each point at which y is the relative maximum and each point at which y is the relative minimum. Justify your answer.
c.) Find the x-coordinate of each point of inflection. Justify your answer.

Answer
Questioner:   Linrosa
Category:  Calculus
Private:  No
 
Subject:  Max and Min, Inflection Points, Symmetry
Question:  1.) Determine the following about the graph of the equation y= (8/x^3)-(6/x).


a.) Is the graph symmetric with respect to the 1.) X-axis? 2.) Y-axis? 3.) Origin?

If it is really a function, you know the answer to (2)

See if  f(-x) = f(x), after simplifying.  If so (1) yes.

See if  f(-x) = - f(x), after simplifying.  If so (3) yes.


b.) Find the x-coordinates of each point at which y is the relative maximum and
each point at which y is the relative minimum. Justify your answer.

Find f'(x).  Set that = 0 and solve, using each solution in:

Find f''(x). Put in each solution.

IF you get f''(x) > 0, min,
IF you get f''(x) < 0, max.


c.) Find the x-coordinate of each point of inflection. Justify your answer.


Find f''(x).  Set = 0 and solve.

That should do it.