Determine the x-coordinate of each critical point of .
A) 0
B) 5
C) 7
D) -5
E) None exist

Question

Determine the x-coordinate of each critical point of  .
A) 0 
B) 5 
C) 7 
D) -5 
E) None exist

Quizplus · Accepted Answer

To find critical points, we need to take the derivative of the function and set it equal to zero. Taking the derivative of the function gives:
-3x^2 + 30x - 60
Setting this equal to zero and solving for x gives:
-3x^2 + 30x - 60 = 0
Dividing by -3 gives:
x^2 - 10x + 20 = 0
Solving this quadratic equation using the quadratic formula gives:
x = 5 ± sqrt(5)
Therefore, there are two critical points at x = 5 + sqrt(5) and x = 5 - sqrt(5). However, only one of them is listed as a choice, so the answer is B) 5.

Determine the X-Coordinate of Each Critical Point of