MTH 274

Question 1

slope of fx=0 at the point (1,2,2)

Answer 1

fx(1,2) says that the slope of the tangent line to the curve at the intersection of the surface z=xy and the plane y=2 at the point (1,2,2) is 0.

Question 2

slope of fy=-7 at the point (1,2,2)

Answer 2

fy(1,2)= -7 says that the slope of the tangent line of the curve at the intersection of the surface z=xy and the plane x=1 at the point (1,2,2) is -7

Question 3

rate of change of fx=0 at the point (1,2,2)

Answer 3

fx(1,2)=0 says that the rate of change of f(x,y) with respect to x with y held constant (value of 2) is 0 units per unit change in x.

Question 4

rate of change of fy= -7 at the point (1,2,2)

Answer 4

fy(1,2) = -7 says that the rate of change of f(x,y) with respect to y with x held constant (value of 1) is -7 units per unit change in y.