## Question

###### 4) Three friends are working on a problem concerning a differentiable function f(x,y,z) at a point...

4) Three friends are working on a problem concerning a differentiable function f(x,y,z) at a point P. While these 3 people are discussing their calculations: 1st person says: "I found the equation of the tangent plane to the surface f(x, y, z)=c at the point P to be 3x + 6y – 2z =9". 2nd person says: "I discovered that the maximum value of the directional derivative of the function f at the point P is 5" 3rd person says: "I calculated the derivative of the function f in the direction of vector ū=i +27 + 2k at the point Pas 11". The fourth person, who heard these people's conversations and has no knowledge about the function f, says: "I think that at least one of the three friends made wrong calculations”. So explain the reason of this fourth person's thought in detail with the calculations you need to do. (15)

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