What can you say about point of inflation for $f(x)=x e^{-3 x}$ ?
A) point of inflation gets closer to $\pm$ 6
B) point of inflation goes away from the origin
C) point of inflation gets closer to the origin
D) point of inflation goes away from $\pm$ 3

Question

Quizplus · Accepted Answer

The point of inflation for a function occurs where the second derivative changes sign. The second derivative of f(x) is given by f''(x) = -18xe^{-3x}, which is negative for x<0 and positive for x>0. Therefore, the point of inflation occurs at x=0, which is the origin. As x moves away from the origin in either direction, the second derivative decreases in magnitude, indicating that the curvature of the function is decreasing. This means that the point of inflation gets closer to the origin as x moves away from it in either direction. Therefore, choice C is correct.

What Can You Say About Point of Inflation For f(x)=xe−3xf(x)=x e^{-3 x}f(x)=xe−3x

What Can You Say About Point of Inflation For $f(x)=x e^{-3 x}$