Maximum slope and deflection of beam

[driedupfish]

Homework Statement

I need to find the max slope and deflection of beams with several different types of loading on them. I need to first find a load function or a moment function. Then use integration (and boundary conditions or continuity conditions) to find an expression for the slope and deflection.

For example, a simple supported beam(6 ft) with a point load at a distance of 4 feet from the starting point. Should I find the moment function from section 0<x<4 ft or 4<x<6 ft?
I think that the max deflection is at x= 4 ft, so should I use a section that includes the point load?

here are the rest of the problems, please give me an idea on which section of the beam to find the moment function for 10.1 - 10.4.

I know how to do the rest, I just don't know which section to cut.

Thanks

 

[pongo38]

I think that you will find the max deflection is at less than 4 ft (but more than 3 ft) from the support. The max deflection would be at 4ft if it were a suspended chain, but this member has stiffness that a chain doesn't have. Once you have the function for M/EI in the range 0 to 4, then integration may get you there, if you can define the boundary conditions. To get the point of max deflection, can you see how to get that using calculus?