Curve:
z = (1/3)ye^x
grad.f (x,y) = (1/3)ye^x i + (1/3)e^x j
Points:
A = ( 0, 0, 0),
B = ( 0, 9, -3)and
C = (-3, -12, -1.99148)
grad f ( 0, 0) = (1/3)(0)(e^0) i + (1/3)(e^0) j
= (1/3) j
Line Segments:
AB = < 0, 9>
mag. of AB = 81^1/2 = 9
u = (AB)/(mag. of AB) = < 0,-1>
grad.f ( 0,0) * u = -1/3
AC = <-3, -12>
mag. of AC = (9 + 144)^1/2 = (153)^1/2 = 12.369...
v = (AC)/(mag. of AC) = (1/12.369...)<-3, -12>
grad.f ( 0,0) * v = -4/12.369... = .323389118
