Question

Find the point of inflection of the following function: (y)/(x)=x²-3x+(6)/(x)

Answer 1

To find the point of inflection of the function y = x² - 3x + 6/x, we must calculate the second derivative and solve for when it equals zero. After finding the second derivative (2 + 12/x³), we discover that there are no real solutions, thus no points of inflection for the function.

Step-by-step explanation:

The question asks us to find the point of inflection for the function y = x² - 3x + 6/x. To find this point, we need to calculate the second derivative of the function and determine where it changes sign, which usually indicates a point of inflection. Let's follow the steps:

1. Find the first derivative (y') of the function: y' = 2x - 3 - 6/x².
2. Find the second derivative (y''): y'' = 2 + 12/x³.
3. Set the second derivative equal to zero and solve for x to find potential points of inflection: 0 = 2 + 12/x³.
4. Upon solving the equation, we find that there are no real values of x that satisfy the equation, meaning there are no points of inflection on the real number line for this function.