. For a function f (at) of a single variable, the existence of the derivative f'(a) at 0. implies that f is continuous at a. In WA2 Q3, we saw that the existence of the partial derivatives f2, and fy of a two-variable function f is not enough to guarantee continuity. Perhaps this can be xed if we require the existence of all the directional derivatives? Let my? New): $2+y4 ifll'ay)#(0a0), 0 if (say) = (0, 0). This is the same f from WA2 Q3. (a) Show that the directional derivative D; f (0,0) of f at (0,0) exist for all unit vectors 11'. [Hint: As a check, you should conrm that D(1,0)f(0,0) matches your computation from WA2. (Which computation?)] (b) In WA2 Q3(b) you showed that f is not continuous. Thus the existence of all directional derivatives does not guarantee continuity. However: if all the directional derivatives of a function g(2:,y) exist and are continuous at (a, b), then 9 must be continuous at (a, b). Explain why