Which of the following is not a correct statement?

When you do conservative work on an object, the work you do is equal to the negative change in potential energy $W_c=-\Delta U$. As an example, if you lift an object against Earth's gravity, the work will be $-mgh$.
Total energy of a system is always conserved, no matter what internal and external forces on the body are present. 

Non- conservative force transfers energy between kinetic energy of the object in motion and the system via energy forms other than potential energy. Total work done by non-conservative force in a closed path motion is not zero.
The negative of the slope of the potential energy curve, for a particle, equals the one-dimensional component of the conservative force on the particle. At an equilibrium point, the slope is zero and is a stable (unstable) equilibrium for a potential energy minimum.