The rational function has
A) a stationary point at x = 1
B) a stationary point at x = -1
C) two stationary points at approximately x = -1.495 and x = 1.495
D) three stationary points approximately at x = 0, x = -1.495 and x = 1.495
E) no stationary points

Question

The rational function  has
A) a stationary point at x = 1 
B) a stationary point at x = -1 
C) two stationary points at approximately x = -1.495 and x = 1.495 
D) three stationary points approximately at x = 0, x = -1.495 and x = 1.495 
E) no stationary points

Quizplus · Accepted Answer

To find stationary points, we need to find the roots of the derivative of the function.

The derivative of the given function is:
(11ead0bc_8d39_dcf6_99a0_d5075745921a_TB6988_11)' = -12x^2/(2x^2+3)^2

Setting the derivative equal to zero and solving for x, we get:
-12x^2/(2x^2+3)^2 = 0
-12x^2 = 0
x = 0

However, x = 0 is not a valid stationary point since it makes the denominator of the original function equal to 0.

To find the valid stationary points, we need to look for the roots of the derivative that are not also roots of the original function.

Using a graphing calculator or computer program to graph the function, we can see that there are two roots of the derivative that are not also roots of the original function, located at approximately x = -1.495 and x = 1.495. Therefore, the answer is C.

The Rational Function Has