an integral
the integral of the derivative of a function
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a three dimensional photograph of the integral of the derivative of a function
the integral of x to the power of 2,
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swapping the derivatives
this defines a minimum in the potential energy curve ( as can be verified either by a graph or by taking another derivative and verifying that it is concave upward at this point ), which means that for values of r slightly smaller than req the slope of the curve is negative ( so the force is positive, repulsive ).,
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