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 is the point where the graph changes concavity from upwards to downwards or vice versa. In this case, we can find the second derivative of the function: 
$$f''(x) = 18xe^{-3x}-18e^{-3x}$$
Setting this equal to zero and solving, we get $x=\frac13$. This is the point of inflection. We can also observe that as $x$ approaches infinity or negative infinity, $f''(x)$ approaches $-\infty$. This means that the graph of $f(x)$ is concave downwards for large positive and negative $x$ values. Therefore, the point of inflection must be getting closer to the origin as $x$ approaches infinity or negative infinity. Thus, the correct choice is C.

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 $f ( x ) = x e ^ { - 3 x }$