Hi all,
I recently had a test with the following question.
At the point B, in the direction of u, is the surface sloping upwards, downwards or
neither? Explain your answer.
the equation of the surface is z = f(x,y) = x^3-6xy+3y^2.
Point B is (-1,1,8).
The gradient vector is -3i+12j
the vector u is -2i+3j
I calculated a slope point B in the direction of u and got +42/sqrt(13).
I was running out of time so simply answered that because the slope was positive, that the surface is sloping upwards. However the amount of marks allocated to the question made me suspicious of the answer being simple, so I thought I'd post here. Hope you guys can help out, and thanks!
I recently had a test with the following question.
At the point B, in the direction of u, is the surface sloping upwards, downwards or
neither? Explain your answer.
the equation of the surface is z = f(x,y) = x^3-6xy+3y^2.
Point B is (-1,1,8).
The gradient vector is -3i+12j
the vector u is -2i+3j
I calculated a slope point B in the direction of u and got +42/sqrt(13).
I was running out of time so simply answered that because the slope was positive, that the surface is sloping upwards. However the amount of marks allocated to the question made me suspicious of the answer being simple, so I thought I'd post here. Hope you guys can help out, and thanks!