Answer:
[tex]x =9[/tex] --- the critical point
Step-by-step explanation:
Given
[tex]f(x) =36x -2x^2[/tex]
Required
Determine the critical numbers
First, we differentiate f(x)
[tex]f'(x) = 36 - 4x[/tex]
Set to 0 and solve for x
[tex]36 -4x = 0[/tex]
Make 4x the subject
[tex]4x = 36[/tex]
Solve for x
[tex]x =36/4[/tex]
[tex]x =9[/tex]
