a. Given f(x,y,z)=x2−2y2+z2,x(t)=sint,y(t)=et and z(t)=3t for 0≤t≤π (i) Find the directional derivative of f(x,y,z) at x

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a. Given f(x,y,z)=x2−2y2+z2,x(t)=sint,y(t)=et and z(t)=3t for 0≤t≤π (i) Find the directional derivative of f(x,y,z) at x=1 in the direction of the vector b=2i+j−2k. Give your answer in terms of π. [9 marks] (ii) Find dtdf​ in terms of t. [4 marks] (iii) Determine the exact value of dtdf​ when x=1. [2 marks] b. A function g(x,y) is defined by g(x,y)=x3−2y2−2y4+3x2y. (i) Show that the function g(x,y) has three stationary points: (0,0), (−1,21​) and (−2,1) [8 marks] (ii) Determine the types of these stationary points, give reason to your answer.