Consider an object following the path of the two-dimensional vector-valued function p(t) = (3t - 212 + 3, - ( 212 + 2+ + 4) ). When does it pass through the point (-2, -4)? If it passes through that point, give the t value. If it does not pass through that point, enter NONE as the answer. Answer: NONE When does it pass through the point (-6, -29)? If it passes through that point, give the t value. If it does not pass through that point, enter NONE as the answer. Answer: NONE When does it pass through the point (-74, -116)? If it passes through that point, give the t value. If it does not pass through that point, enter NONE as the answer. Answer: NONE When is it at rest? If it is at rest at some point, give the t value. If it is never at rest, enter NONE as the answer. Answer: 2/3Let f (x, y, z) = xy + y z+ z x and a = (-2,4,-4) Then: a. fx(a) = 16 b. fy(a) = -12 c. fz(a) = 4 d. Df (a) = 16 -12 4 16 e. Vf(a) -12 4For the point ( - 2 , - 4 ) - (3 t - 2+ + 3 , - ( 24 + 2 + + 4 ) ) = ( - 2 , -4 ) 3t - 2+ +3 =-2 ARE + 2 + + 4 ) = 4 4 =) 2t-34-5=0 -7 24- 5+ +26 - 5= 0 - 2t + 2 t + 4 = 4 7 t ( 2t - 5 ) +1 ( 2t - 5 ) -0 ") 26 + 2 t = 0 - ) ( + + 1 ) ( 24 - 5 ) = 0 5 tt t = 0 7 + ( t + 1 ) = 0 9 t = -1 - t = and t = 2 and t = - 1 Here we can see that t= -1 is a Common value So , the object passes the given point (- 2, -4) when t = - 1