The curve x+y=4 is defined for x≥0,y≥0.
a. (i) Show that dxdy=−xy.
b. (ii) Prove that the curve possesses exactly one horizontal tangent and exactly one vertical tangent, and determine their coordinates.
c. (iii) Write the equations of the horizontal and vertical tangents obtained in part (ii).
d. (iv) For 0<x<16, discuss the sign (positive or negative) of the slope dxdy and hence comment on the overall orientation of the curve in this interval.