Ture or false A)Suppose S is a surface with equation f(x,y,z)=k . Then the norma

Question

Ture or false

A)Suppose S is a surface with equation f(x,y,z)=k . Then the normal line to S at the point (a, b, c) is parallel to the vector <fx(a,b,c),fy(a,b,c),fz(a,b,c)>

b)The directional derivative of f at (a,b) in the direction of the unit vector U is the slope of the tangent line to the graph of f at the point (a,b,f(a,b) in the direction of U

c)If f(x,y)=2x+3y, then f(x,y)=<2,3>

d) The directional derivative of f at (a,b) in the direction of the unit vector U is the slope of the tangent line to the graph of f at the point (a,b,f(a,b) in the direction of <a,b,f(a,b)>.

e)If f(x,y)=(x^2)y+3cos(x), then f(x,y)=2xy-3sin(x)+x^2

f)Suppose f(x,y)=3x+9y. Then for any point (x, y) the directional derivative duf(x,y) is smallest when U points in the same direction as the vector <3,9> .

g)If f(x,y)=(x^2)y+3cos(x), then f(x,y)=<2xy-3sin(x),x^2>

h)If f(x,y)=2x+3xy-y^2 and u=<3/5,4/5>, then duf(x,y)=3(2+3y)+4(3x-2y).

i)If f(x,y)=(x^2)y+3cos(x) , then f(x,y)=<2xy+3sin(x),x^2>.

j)If f(x,y)=2x+3y, then f(x,y)=2+3.

Explanation / Answer

A - True

B- True

C - Rewrite the statement once it is not clear( I feel it is gradient if so it is true)

D- False

E - Statement is not clear rewrite

F- false it attains maximum in this direction.

G- I feel it is gradient if so it is true

H- false

I- I feel it is gradient if so it is False

j - doesnt make sence.(statement need to complete)Technical words are missing

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