The slope of the tangent to the graph of the functions y = x ^ 2/2 + 2 / x at the point x = -1 is.

The slope of a tangent at a particular point is equal to the value of the derivative at that point.

Let’s calculate the derivative of the function, first transforming it.

y = x² / 2 + 2 / x = 1/2 * x² + 2 * x-1.

y ‘= 1/2 * 2 * x + 2 * (-1) * x-1-1 = x – 2 * x-2 = x – 2 / x² = (x3 – 2) / x².

Let’s calculate the value of the derivative at the point x = -1.

y ‘(- 1) = ((-1) 3 – 2) / (- 1) ² = (-1 – 2) / 1 = -3.

Answer: The slope of the tangent at the point x = -1 is -3.