Question

(e) none of the above 6. True or false, 2 pts each. If the statement is ever false, circle false as your answer. No work is required, and no partial credit will be given. (a) f(a, b) points in the direction of greatest increase of f at (a,b). TRUE FALSE (b) If a and b are three-dimensional vectors, then so is a b. TRUE FALSE (C) For any two vectors a and b, a + b = a + bl. TRUE FALSE (d) If the directional derivative of f in the direction of a unit vector u, i.e. Duf(x,y) = 0, then f(x, y) = 0. TRUE FALSE (e) If f(t, y) = Iny, then Vf(,y) = - TRUE FALSE

Answer 1

6) a) of (a, b) point in the direction of greatest increase off at (a,b). false. It can point in the direct reatest decreate at (a,b). b) a,b ER² , then ab ER². False dot product is a scalar not a vector c) for any tworectors a,b, latb=altlbl False a=(-1,-1), b=(1,1) , atb=(0,0), latb) = (0,0) lal =(1,1), 161 = (1,1),laltbl= (2,2) If directional off in the direction of a wonit vector uie Duf(x,y)=0 then f(2,4)=0 false let flasy)= nty, let (Ay) = (1, 1), U=(11 - 11 Dufcr,y) = (1,1) ( ) = ta ta = 0 but flasy) & 0 e) Iff f(x,y) = lay then of (dy) = Yy false vfCmy) - ) -(0)