Introduction:
A simply supported beam is a structural element that is supported on both ends and has no moment resistance at the supports. In this problem, we have a simply supported beam with a span of 4m and a point load of 4 kN applied at a distance of 3m from the left support. We need to determine where the maximum slope occurs in the beam.

Analysis:
To analyze the beam, we need to consider the equations of equilibrium and the relationship between the bending moment and the slope of the beam.

1. Equations of equilibrium:
The sum of the forces in the vertical direction must be equal to zero. Since the beam is simply supported, the reactions at the supports will balance the applied load.

2. Relationship between bending moment and slope:
The slope of the beam at any point is related to the bending moment at that point. The slope is the first derivative of the deflection equation, and the bending moment is the second derivative of the deflection equation.

Maximum slope:
The maximum slope in a simply supported beam occurs at the point of maximum bending moment. The bending moment is maximum at the support where the point load is applied. Therefore, the maximum slope occurs at the right support.

Explanation:
The maximum slope occurs at the right support because that is where the bending moment is maximum. The point load creates a clockwise bending moment at the right support, causing the beam to deflect downwards. The slope of the beam is maximum at the right support because the deflection is largest at that point.

At the left support, the bending moment is zero because there are no external loads or moments applied at that point. Therefore, the slope is also zero at the left support.

At mid-span, the bending moment is also zero because the load is symmetrically placed with respect to the supports. Therefore, the slope is also zero at mid-span.

Hence, the maximum slope occurs at the right support, which is option B in the given choices.