Find the stationary points of the function y = 2x3 + 5 and determine their nature.

Given the function $y = 2x^3 + 5$.
Differentiate $y$ with respect to $x$:

$$\frac{dy}{dx} = \frac{d}{dx}(2x^3 + 5) = 6x^2$$

$$6x^2 = 0$$ $$x^2 = 0$$ $$x = 0$$

There is one stationary point at $x=0$.

$$y = 2(0)^3 + 5 = 0 + 5 = 5$$

The stationary point is $(0, 5)$.

Differentiate $\frac{dy}{dx} = 6x^2$ with respect to $x$:

$$\frac{d^2y}{dx^2} = \frac{d}{dx}(6x^2) = 12x$$

$$\frac{d^2y}{dx^2} \Big|_{x=0} = 12(0) = 0$$

Since the second derivative is 0, we need to check the sign of the first derivative around $x=0$ to confirm the nature of the point.
For $x < 0$ (e.g., $x = -1$), $\frac{dy}{dx} = 6(-1)^2 = 6 > 0$.
For $x > 0$ (e.g., $x = 1$), $\frac{dy}{dx} = 6(1)^2 = 6 > 0$.
Since the sign of $\frac{dy}{dx}$ does not change around $x=0$ (it remains positive), the point $(0, 5)$ is a point of inflection.

The stationary point is $\text{(0, 5) which is a point of inflection}$.