Find all points of inflection on the graph of the function .

Question

Find all points of inflection on the graph of the function  . ​

Quizplus · Accepted Answer

The points of inflection occur where the second derivative of the function changes sign. We can find the second derivative of this function to be 11e^x - 3e^(-x), which is positive for all x. Therefore, the second derivative does not change sign and there are no points of inflection except at the endpoints of the domain. The domain is all real numbers, so the only possible points of inflection are at positive and negative infinity. Since the function approaches 0 as x approaches positive or negative infinity, there are no points of inflection. However, some answer choices include extraneous information that may confuse the reader. For example, answer choices A, B, and C include random strings of characters after the mathematical expression, which are irrelevant and may discourage students from choosing answer D.

Find All Points of Inflection on the Graph of the Function