Chapter 23.5, Problem 23.5TYU

In a certain region of space the potential is given by V = A + Bx + Cy³ + Dxy, where A, B, C, and D are positive constants. Which of these statements about the electric field $\stackrel{\to }{E}$ in this region of space is correct? (There may be more than one correct answer.) (i) Increasing the value of A will increase the value of $\stackrel{\to }{E}$ at all points; (ii) increasing the value of A will decrease the value of $\stackrel{\to }{E}$ at all points; (iii) $\stackrel{\to }{E}$ has no z-component; (iv) the electric field is zero at the origin (x = 0, y = 0, z = 0).