Determine all critical points for the function.
-$$f ( x ) = x ^ { 2 } + 12 x + 36$$
A) x = -12
B) x = -6
C) x = 6
D) x = 0

Question

Quizplus · Accepted Answer

To find the critical points of the function $f(x) = x^2 + 12x + 36$, we first need to find its derivative and then solve for $x$ when the derivative is equal to zero. The derivative of $f(x)$ is $f'(x) = 2x + 12$. Setting this equal to zero gives $2x + 12 = 0$, which simplifies to $x = -6$. Therefore, the critical point of the function is $x = -6$.

Determine All Critical Points for the Function f(x)=x2+12x+36f ( x ) = x ^ { 2 } + 12 x + 36f(x)=x2+12x+36

Determine All Critical Points for the Function $f ( x ) = x ^ { 2 } + 12 x + 36$