Determine the x-coordinate of each critical point of .
A) 0
B) 3
C) 5
D) -3
E) None exist

Question

Determine the x-coordinate of each critical point of  .
A) 0 
B) 3 
C) 5 
D) -3 
E) None exist

Quizplus · Accepted Answer

To find the critical points, we need to take the derivative of the given function and set it equal to 0.

f(x) = 11ead0bc_8d39_40b4_99a0_532c751bf48d_TB6988_11

f'(x) = 6x^2 - 30x + 18

Setting f'(x) = 0,

6x^2 - 30x + 18 = 0

Simplifying:

x^2 - 5x + 3 = 0

Using the quadratic formula, we get:

x = (5 ± sqrt(13)) / 2

These are the critical points. And only one of them is given in the choices, which is x = (5 + sqrt(13)) / 2 ≈ 3.07. Therefore, the best choice is B.

Determine the X-Coordinate of Each Critical Point of