If the first derivative is the slope at a point and the first integral is the area under the curve, then what is the second derivative?

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If the first derivative of the function $y(x)$, $$\frac{dy}{dx}$$, is the slope at a point and the first indefinite integral $$\int dx y(x)$$ is the area under the curve, then what is the geometric meaning of the second derivative?

$$\frac{d^2y}{dx^2}$$

or the second indefinite integral ?

$$\int dx \int dx y$$

is there some geometric sense in which to understand/interpret the general differential or integral operator?