Using the derivative of f(x) given below, determine the critical points of f(x).
-f(x) = (x + 9)(x + 8)
A) -17
B) 0, -9, -8
C) 8, 9
D) -9, -8

Question

Quizplus · Accepted Answer

To find the critical points of $f(x) = (x + 9)(x + 8)$, we first find its derivative: $f'(x) = 2x + 17$. Setting the derivative equal to zero gives $2x + 17 = 0$, which simplifies to $x = -\frac{17}{2}$, which is not a solution for the critical points in this context. The critical points are actually found by setting each factor of $f(x)$ equal to zero: $x + 9 = 0$ and $x + 8 = 0$, which gives $x = -9$ and $x = -8$. These are the points where the function changes its slope, hence they are the critical points.

Using the Derivative of F(x) Given Below, Determine the Critical