ESE 318-01 Exam 3, Apr. 12, 2018 NAME:___59 papers received from 60 enrolled__ Problem 1. (20 points)Consider the scalar functionzzeyxyexzyxF2222,,and the point P= (1, 1, 0).(a)Find the direction in which Fis increasing fastest from P. (b)Find the rate of that maximum increase. (c)Find the rate of increase of Ffrom Ptoward the point (-1,4,6). (d)Find FofLaplaciangradFdivFat P. 3416990,1,14,3,322,21,120,1,122,2,2222222FbFaeyexyexyxeFzzzz 7277249636946,3,24,3,36,3,20,1,16,4,1FDirbcb 1234144422222222222yxeeyexeeFdzzzzzGrading: 21 papers earned all 20 points and another 18 earned 19 points with the only error being to fail to evaluate the Laplacian at the point P. 5 points per part, in general. Only 7 papers earned fewer than 16 points, and only 1 below 12. Gradient or Laplacian not evaluated at P: -1 point. “Sloppy” error: -1 to -2 pts. Sign error on (c) due to backward direction: -2 pts. Method/approach seriously bad or botched: -3 to -5 pts per part.