$\text { Find the critical number of the function } f ( x ) = - 6 x ^ { 2 } + 108 x + 7$
A) $x = 18$
B) $x = 9$
C) $x = 84$
D) $x = 14$
E) $x = 7$

Question

$\text { Find the critical number of the function } f ( x ) = - 6 x ^ { 2 } + 108 x + 7$ 
A) $x = 18$
B) $x = 9$
C) $x = 84$
D) $x = 14$
E) $x = 7$

Quizplus · Accepted Answer

To find the critical numbers, we need to find the values of x for which f'(x) = 0 or f'(x) is undefined. 
Taking the derivative of f(x), we get: 
f'(x) = -12x + 108

Setting f'(x) = 0, we get: 
-12x + 108 = 0 
-12(x - 9) = 0 
x = 9

Therefore, x = 9 is a critical number of the function f(x).

Find the critical number of the function f(x)=−6x2+108x+7\text { Find the critical number of the function } f ( x ) = - 6 x ^ { 2 } + 108 x + 7 Find the critical number of the function f(x)=−6x2+108x+7

$\text { Find the critical number of the function } f ( x ) = - 6 x ^ { 2 } + 108 x + 7$