Chapter 7.4, Problem 7.4TYU

A particle moving along the x-axis is acted on by a conservative force F_x. At a certain point, the force is zero. (a) Which of the following statements about the value of the potential-energy function U(x) at that point is correct? (i) U(x) = 0; (ii) U(x) > 0; (iii) U(x) < 0; (iv) not enough information is given to decide. (b) Which of the following statements about the value of the derivative of U(x) at that point is correct? (i) dU(x)/dx = 0; (ii) dU(x)/dx > 0; (iii) dU(x)/dx < 0; (iv) not enough information is given to decide.