Determine all critical points for the function.
-$$f ( x ) = ( x - 6 ) ^ { 7 }$$
A) x = 0, x = 6, and x = 7
B) x = 6 and x = 7
C) x = 0 and x = 6
D) x = 6

Question

Quizplus · Accepted Answer

To find critical points, we need to find where the derivative of the function equals zero or where it is undefined. 
$$f'(x) = 7(x-6)^6 \cdot 1$$
Setting this equal to zero, we get:
$$7(x-6)^6 = 0$$
Since a number raised to a power of 6 can never be zero, we know that the only solution to this equation is when x = 6. Therefore, x = 6 is the only critical point.

Determine All Critical Points for the Function f(x)=(x−6)7f ( x ) = ( x - 6 ) ^ { 7 }f(x)=(x−6)7

Determine All Critical Points for the Function $f ( x ) = ( x - 6 ) ^ { 7 }$