Let P(f, w) be a model for the population (of cells) in a petri dish after 1 month as a function of food f (in mg) and water w (in mL). A. Give the correct units for the following values: (a) P(20,50) 10,000. (b) P,(20,50) = 1,500. (c) P (20,50)=2,400 (d) P(20, 50)=500, (e) P(20, 50)-800, Verify that f(x,y) equation fa+fy = 0. In(2+ y) is a solution to the partial differential Consider the surface in R defined by 2-=2+yz. A. Find a vector normal to the surface at the point (1,-1,2). B. Find an equation for the plane tangent to the surface at the point (1,-1,2) Does the function f(x,y)=3x - 6xy+y have any local minimums or any local maximums? If so, where?