#3. The Gradient and Directional Derivatives (a) Calculate the derivative of F(x,y,z) = x + 3xy-z...

 

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#3. The Gradient and Directional Derivatives (a) Calculate the derivative of F(x,y,z) = x + 3xy-z + 2y +z+4 at Po (0,0,0) in the direction of vi+j+k. ritical point for and explain why not solve the given problem. The optimization problem, finding both the ndaninimum values off, two ways (b) Is F increasing or decreasing in this direction? by subst (c) Find the direction (from Po) in which F changes the fastest, and calculate the maximal rate of change of F at Po. #3. The Gradient and Directional Derivatives (a) Calculate the derivative of F(x,y,z) = x + 3xy-z + 2y +z+4 at Po (0,0,0) in the direction of vi+j+k. ritical point for and explain why not solve the given problem. The optimization problem, finding both the ndaninimum values off, two ways (b) Is F increasing or decreasing in this direction? by subst (c) Find the direction (from Po) in which F changes the fastest, and calculate the maximal rate of change of F at Po.