1.- Describe the steps to follow to calculate the minimum, maximum and inflection points of a function. 2.- Solve and make the corresponding graph. Imagine that you are hired in a company and you are asked to make the design of a metal plate that will serve as heating for an industrial use, in particular you are asked to determine the rate of change of the temperature with respect to the distance in a point (2,1) in both the x and y directions. Consider that the temperature at a point (x_,yi is given by 11:, y) - (\"yhthe temperature is measured in C and the variables x, y in meters} 3.- Find the volume of the solid bounded by the plane x=3 And the parabolic trough: z= 4-y2. 4.- Applying the Divergence Theorem or Gauss's Theorem, calculate the flux from F to through the surface S that represents the boundary of the solid E. 39 F(x.y,z) = (x+ e?'f+ 2r2 +x2j+ z2 +xyk) E is the solid bounded by the surfaces 2 = J2 x2 y2 : and also for Z = X2 + J" 5.- Determine the critical points (maximum, minimum and saddle points from the following function. may) = :3 +xy3-2xy-5x